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  Subjects -> MATHEMATICS (Total: 969 journals)
    - APPLIED MATHEMATICS (84 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (22 journals)
    - PROBABILITIES AND MATH STATISTICS (86 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 28)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 5)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)

        1 2 3 4 | Last

Journal Cover European Journal of Combinatorics
  [SJR: 1.233]   [H-I: 35]   [5 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0195-6698 - ISSN (Online) 1095-9971
   Published by Elsevier Homepage  [3175 journals]
  • On the number of labeled graphs of bounded treewidth
    • Authors: Julien Baste; Marc Noy; Ignasi Sau
      Pages: 12 - 21
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Julien Baste, Marc Noy, Ignasi Sau
      Let T n , k be the number of labeled graphs on n vertices and treewidth at most k (equivalently, the number of labeled partial k -trees). We show that c k 2 k n log k n 2 − k ( k + 3 ) 2 k − 2 k − 2 ≤ T n , k ≤ k 2 k n n 2 − k ( k + 1 ) 2 k − k , for k > 1 and some explicit absolute constant c > 0 . Disregarding terms depending only on k , the gap between the lower and upper bound is of order ( log k ) n . The upper bound is a direct consequence of the well-known formula for the number of labeled k -trees, while the lower bound is obtained from an explicit construction. It follows from this construction that both bounds also apply to graphs of pathwidth and proper-pathwidth at most k .

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.030
      Issue No: Vol. 71 (2018)
       
  • On the irregularity of uniform hypergraphs
    • Authors: Lele Liu; Liying Kang; Erfang Shan
      Pages: 22 - 32
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Lele Liu, Liying Kang, Erfang Shan
      Let H be an r -uniform hypergraph on n vertices and m edges, and let d i be the degree of i ∈ V ( H ) . Denote by ε ( H ) the difference between the spectral radius of H and the average degree of H . Also, denote s ( H ) = ∑ i ∈ V ( H ) d i − r m n , v ( H ) = 1 n ∑ i ∈ V ( H ) d i r r − 1 − r m n r r − 1 . In this paper, we investigate the irregularity of r -uniform hypergraph H with respect to ε ( H ) , s ( H ) and v ( H ) , which extend relevant results to uniform hypergraphs.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.034
      Issue No: Vol. 71 (2018)
       
  • On the largest sizes of certain simultaneous core partitions with distinct
           parts
    • Authors: Huan Xiong
      Pages: 33 - 42
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Huan Xiong
      We derive the largest sizes of ( t , m t + 1 ) and ( t , m t − 1 ) -core partitions with distinct parts, and prove that the numbers of such partitions with the largest sizes are at most 2. This work is motivated by Amdeberhan’s conjecture on ( t , t + 1 ) -core partitions with distinct parts and subsequent research on the enumeration, largest sizes and the average sizes of simultaneous core partitions with distinct parts.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.031
      Issue No: Vol. 71 (2018)
       
  • On multicolor Ramsey numbers for loose k-paths of length three
    • Authors: Tomasz Łuczak; Joanna Polcyn; Andrzej Ruciński
      Pages: 43 - 50
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Tomasz Łuczak, Joanna Polcyn, Andrzej Ruciński
      We show that there exists an absolute constant A such that for each k ≥ 2 and every coloring of the edges of the complete k -uniform hypergraph on A r vertices with r colors, r ≥ r k , one of the color classes contains a loose path of length three.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.033
      Issue No: Vol. 71 (2018)
       
  • A note on diameter-Ramsey sets
    • Authors: Jan Corsten; Nóra Frankl
      Pages: 51 - 54
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Jan Corsten, Nóra Frankl
      A finite set A ⊂ R d is called diameter-Ramsey if for every r ∈ N , there exists some n ∈ N and a finite set B ⊂ R n with diam ( A ) = diam ( B ) such that whenever B is coloured with r colours, there is a monochromatic set A ′ ⊂ B which is congruent to A . We prove that sets of diameter 1 with circumradius larger than 1 ∕ 2 are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than 135° are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher and Rödl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.036
      Issue No: Vol. 71 (2018)
       
  • Shuffles of trees
    • Authors: Eric Hoffbeck; Ieke Moerdijk
      Pages: 55 - 72
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Eric Hoffbeck, Ieke Moerdijk
      We discuss a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. We give several equivalent descriptions, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets, but our presentation is independent and entirely self-contained.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.035
      Issue No: Vol. 71 (2018)
       
  • Combinatorial proofs of some properties of tangent and Genocchi numbers
    • Authors: Guo-Niu Han; Jing-Yi Liu
      Pages: 99 - 110
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Guo-Niu Han, Jing-Yi Liu
      The tangent number T 2 n + 1 is equal to the number of increasing labelled complete binary trees with 2 n + 1 vertices. This combinatorial interpretation immediately proves that T 2 n + 1 is divisible by 2 n . However, a stronger divisibility property is known in the studies of Bernoulli and Genocchi numbers, namely, the divisibility of ( n + 1 ) T 2 n + 1 by 2 2 n . The traditional proofs of this fact need significant calculations. In the present paper, we provide a combinatorial proof of the latter divisibility by using the hook length formula for trees. Furthermore, our method is extended to k -ary trees, leading to a new generalization of the Genocchi numbers.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.041
      Issue No: Vol. 71 (2018)
       
  • Minimum rainbow H-decompositions of graphs
    • Authors: Lale Özkahya; Yury Person
      Pages: 111 - 124
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Lale Özkahya, Yury Person
      Given graphs G and H , we consider the problem of decomposing a properly edge-colored graph G into few parts consisting of rainbow copies of H and single edges. We establish a close relation to the previously studied problem of minimum H -decompositions, where an edge coloring does not matter and one is merely interested in decomposing graphs into copies of H and single edges.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.03.002
      Issue No: Vol. 71 (2018)
       
  • Smooth Schubert varieties in the affine flag variety of type Ã
    • Authors: Edward Richmond; William Slofstra
      Pages: 125 - 138
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Edward Richmond, William Slofstra
      We show that every smooth Schubert variety of affine type A ̃ is an iterated fibre bundle of Grassmannians, extending an analogous result by Ryan and Wolper for Schubert varieties of finite type A . As a consequence, we finish a conjecture of Billey–Crites that a Schubert variety in affine type A ̃ is smooth if and only if the corresponding affine permutation avoids the patterns 4231 and 3412. Using this iterated fibre bundle structure, we compute the generating function for the number of smooth Schubert varieties of affine type A ̃ .

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.03.003
      Issue No: Vol. 71 (2018)
       
  • On splitting digraphs
    • Authors: Donglei Yang; Yandong Bai; Guanghui Wang; Jianliang Wu
      Pages: 174 - 179
      Abstract: Publication date: June 2018
      Source:European Journal of Combinatorics, Volume 71
      Author(s): Donglei Yang, Yandong Bai, Guanghui Wang, Jianliang Wu
      In 1995, Stiebitz asked the following question: For any positive integers s , t , is there a finite integer f ( s , t ) such that every digraph D with minimum out-degree at least f ( s , t ) admits a bipartition ( A , B ) such that A induces a subdigraph with minimum out-degree at least s and B induces a subdigraph with minimum out-degree at least t ' We give an affirmative answer for tournaments, multipartite tournaments, and digraphs with bounded maximum in-degrees. In particular, we show that for every ϵ with 0 < ϵ < 1 ∕ 2 , there exists an integer δ 0 such that every tournament with minimum out-degree at least δ 0 admits a bisection ( A , B ) , so that each vertex has at least ( 1 ∕ 2 − ϵ ) of its out-neighbors in A , and in B as well.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.03.005
      Issue No: Vol. 71 (2018)
       
  • Planar triangulations, bridgeless planar maps and Tamari intervals
    • Authors: Wenjie Fang
      Pages: 75 - 91
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Wenjie Fang
      We present a direct bijection between planar 3-connected triangulations and bridgeless planar maps, which were first enumerated by Tutte (1962) and Walsh and Lehman (1975) respectively. Previously known bijections by Wormald (1980) and Fusy (2010) are all defined recursively. Our direct bijection passes by a new class of combinatorial objects called “sticky trees”. We also present bijections between sticky trees, intervals in the Tamari lattices and closed flows on forests. With our bijections, we recover several known enumerative results about these objects. We thus show that sticky trees can serve as a nexus of bijective links among all these equi-enumerated objects.

      PubDate: 2018-01-09T19:28:15Z
      DOI: 10.1016/j.ejc.2017.12.002
      Issue No: Vol. 70 (2018)
       
  • A bijective proof of the Shor recurrence
    • Authors: Victor J.W. Guo
      Pages: 92 - 98
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Victor J.W. Guo
      In an approach to the Cayley formula for counting trees, Shor discovered a refined recurrence relation concerning the number of improper edges. Chen and the author gave a bijection for the Shor recurrence based on the combinatorial interpretations of Zeng, answering a question of Shor. In this paper, we present a new bijective proof of the Shor recurrence by applying Shor’s formula for counting forests of rooted trees with roots 1 , … , r and with a given number of improper edges.

      PubDate: 2018-01-09T19:28:15Z
      DOI: 10.1016/j.ejc.2017.12.004
      Issue No: Vol. 70 (2018)
       
  • Colourings without monochromatic disjoint pairs
    • Authors: Dennis Clemens; Shagnik Das; Tuan Tran
      Pages: 99 - 124
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Dennis Clemens, Shagnik Das, Tuan Tran
      The typical extremal problem asks how large a structure can be without containing a forbidden substructure. The Erdős–Rothschild problem, introduced in 1974 by Erdős and Rothschild in the context of extremal graph theory, is a coloured extension, asking for the maximum number of colourings a structure can have that avoid monochromatic copies of the forbidden substructure. The celebrated Erdős–Ko–Rado theorem is a fundamental result in extremal set theory, bounding the size of set families without a pair of disjoint sets, and has since been extended to several other discrete settings. The Erdős–Rothschild extensions of these theorems have also been studied in recent years, most notably by Hoppen, Koyakayawa and Lefmann for set families, and Hoppen, Lefmann and Odermann for vector spaces. In this paper we present a unified approach to the Erdős–Rothschild problem for intersecting structures, which allows us to extend the previous results, often with sharp bounds on the size of the ground set in terms of the other parameters. In many cases we also characterise which families of vector spaces asymptotically maximise the number of Erdős–Rothschild colourings, thus addressing a conjecture of Hoppen, Lefmann and Odermann.

      PubDate: 2018-01-09T19:28:15Z
      DOI: 10.1016/j.ejc.2017.12.006
      Issue No: Vol. 70 (2018)
       
  • Eigenvalues of subgraphs of the cube
    • Authors: Béla Bollobás; Jonathan Lee; Shoham Letzter
      Pages: 125 - 148
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Béla Bollobás, Jonathan Lee, Shoham Letzter
      We consider the problem of maximising the largest eigenvalue of subgraphs of the hypercube Q d of a given order. We believe that in most cases, Hamming balls are maximisers, and our results support this belief. We show that the Hamming balls of radius o ( d ) have largest eigenvalue that is within 1 + o ( 1 ) of the maximum value. We also prove that Hamming balls with fixed radius maximise the largest eigenvalue exactly, rather than asymptotically, when d is sufficiently large. Our proofs rely on the method of compressions.

      PubDate: 2018-01-09T19:28:15Z
      DOI: 10.1016/j.ejc.2017.12.007
      Issue No: Vol. 70 (2018)
       
  • An isoperimetric inequality for antipodal subsets of the discrete cube
    • Authors: David Ellis; Imre Leader
      Pages: 149 - 154
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): David Ellis, Imre Leader
      We say a family of subsets of { 1 , 2 , … , n } is antipodal if it is closed under taking complements. We prove a best-possible isoperimetric inequality for antipodal families of subsets of { 1 , 2 , … , n } (of any size). Our inequality implies that for any k ∈ N , among all such families of size 2 k , a family consisting of the union of two antipodal ( k − 1 ) -dimensional subcubes has the smallest possible edge boundary.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2017.12.003
      Issue No: Vol. 70 (2018)
       
  • Occurrence of right angles in vector spaces over finite fields
    • Authors: Michael Bennett
      Pages: 155 - 163
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Michael Bennett
      Here we examine some Erdős–Falconer-type problems in vector spaces over finite fields involving right angles. Our main goals are to show that (a) a subset A ⊂ F q d of size ≥ c q d + 2 3 contains three points which generate a right angle, and (b) a subset A ⊂ F q d of size ≥ C q d + 2 2 contains two points which generate a right angle with the vertex at the origin. We will also prove that (b) is sharp up to constants and provide some partial results for similar problems related to spread and collinear triples.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2017.12.005
      Issue No: Vol. 70 (2018)
       
  • The flow index and strongly connected orientations
    • Authors: Jiaao Li; Carsten Thomassen; Yezhou Wu; Cun-Quan Zhang
      Pages: 164 - 177
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Jiaao Li, Carsten Thomassen, Yezhou Wu, Cun-Quan Zhang
      We prove that, for any natural number p , the flow index ϕ ( G ) < 2 + 1 p if and only if G has a strongly connected modulo ( 2 p + 1 ) -orientation. For the case p = 1 we prove that the flow index of every 8-edge-connected graph is strictly less than 3.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2017.12.009
      Issue No: Vol. 70 (2018)
       
  • Vexillary degeneracy loci classes in K-theory and algebraic cobordism
    • Authors: Thomas Hudson; Tomoo Matsumura
      Pages: 190 - 201
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Thomas Hudson, Tomoo Matsumura
      In this paper, we prove determinantal formulas for the K -theory classes of the structure sheaves of degeneracy loci associated to vexillary permutations in type A . As a consequence we obtain determinantal formulas for Lascoux–Schützenberger’s double Grothendieck polynomials associated to vexillary permutations. We also prove a generalization of the formula in algebraic cobordism.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.001
      Issue No: Vol. 70 (2018)
       
  • Restricted inversion sequences and enhanced 3-noncrossing partitions
    • Authors: Zhicong Lin
      Pages: 202 - 211
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Zhicong Lin
      We prove a conjecture due independently to Yan and Martinez–Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-noncrossing partitions have the same cardinality. Our approach applies both the generating tree technique and the so-called obstinate kernel method developed by Bousquet-Mélou. One application of this equinumerosity is a discovery of an intriguing identity involving numbers of classical and enhanced 3-noncrossing partitions.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.002
      Issue No: Vol. 70 (2018)
       
  • Highly connected subgraphs of graphs with given independence number
    • Authors: Shinya Fujita; Henry Liu; Amites Sarkar
      Pages: 212 - 231
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Shinya Fujita, Henry Liu, Amites Sarkar
      Let G be a graph on n vertices with independence number α . We prove that if n is sufficiently large ( n ≥ α 2 k + 1 will do), then G always contains a k -connected subgraph on at least n ∕ α vertices. The value of n ∕ α is sharp, since G might be the disjoint union of α equally-sized cliques. For k ≥ 3 and α = 2 , 3 , we shall prove that the same result holds for n ≥ 4 ( k − 1 ) and n ≥ 27 ( k − 1 ) 4 respectively, and that these lower bounds on n are sharp.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.004
      Issue No: Vol. 70 (2018)
       
  • Construction of strongly regular Cayley graphs based on three-valued Gauss
           periods
    • Authors: Koji Momihara
      Pages: 232 - 250
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Koji Momihara
      In this paper, we give a construction of strongly regular Cayley graphs on the additive groups of finite fields based on three-valued Gauss periods. As consequences, we obtain two infinite families and one sporadic example of new strongly regular Cayley graphs. This construction can be viewed as a generalization of that of strongly regular Cayley graphs obtained in Bamberg et al. (0000).

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.007
      Issue No: Vol. 70 (2018)
       
  • On a theorem of Deshouillers and Freiman
    • Authors: R. Balasubramanian; Prem Prakash Pandey
      Pages: 284 - 296
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): R. Balasubramanian, Prem Prakash Pandey
      The “structure theory of set addition” has been well studied in the last fifty years, after the works of Freiman. In [1] Deshouillers and Freiman established a structure theorem for subsets of Z ∕ n Z with small doubling constant. In this article we provide a simpler proof of the structure theorem of [1], and on our way we also obtain some improvements.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2017.12.008
      Issue No: Vol. 70 (2018)
       
  • Rainbow matchings in edge-colored complete split graphs
    • Authors: Zemin Jin; Kecai Ye; Yuefang Sun; He Chen
      Pages: 297 - 316
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Zemin Jin, Kecai Ye, Yuefang Sun, He Chen
      In 1973, Erdős et al. introduced the anti-Ramsey number for a graph G in K n , which is defined to be the maximum number of colors in an edge-coloring of K n which does not contain any rainbow G . This is always regarded as one of rainbow generalizations of the classic Ramsey theory. Since then the anti-Ramsey numbers for several special graph classes in complete graphs have been determined. Also, the researchers generalized the host graph for the anti-Ramsey number from the complete graph to general graphs, including bipartite graphs, complete split graphs, planar graphs, and so on. In this paper, we study the anti-Ramsey number of matchings in the complete split graph. Since the complete split graph contains the complete graph as a subclass, the results in this paper cover the previous results about the anti-Ramsey number of matchings in the complete graph.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.010
      Issue No: Vol. 70 (2018)
       
  • Overpartitions with bounded part differences
    • Authors: Shane Chern; Ae Ja Yee
      Pages: 317 - 324
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Shane Chern, Ae Ja Yee
      We generalize recent results of Breuer and Kronholm, and Chern on partitions and overpartitions with bounded differences between largest and smallest parts. We prove our generalization both analytically and combinatorially.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.003
      Issue No: Vol. 70 (2018)
       
  • Factorial characters of the classical Lie groups
    • Authors: Angèle M. Foley; Ronald C. King
      Pages: 325 - 353
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Angèle M. Foley, Ronald C. King
      Just as the definition of factorial Schur functions as a ratio of determinants allows one to show that they satisfy a Jacobi–Trudi-type identity and have an explicit combinatorial realisation in terms of semistandard tableaux, so we offer here definitions of factorial irreducible characters of the classical Lie groups as ratios of determinants that share these two features. These factorial characters are each specified by a partition, λ = ( λ 1 , λ 2 , … , λ n ) , and in each case a flagged Jacobi–Trudi identity is derived that expresses the factorial character as a determinant of corresponding factorial characters specified by one-part partitions, ( m ) , for which we supply generating functions. These identities are established by manipulating determinants through the use of certain recurrence relations derived from these generating functions. The transitions to combinatorial realisations of the factorial characters in terms of tableaux are then established by means of non-intersecting lattice path models. The results apply to g l ( n ) , s o ( 2 n + 1 ) , s p ( 2 n ) and o ( 2 n ) , and are extended to the case of s o ( 2 n ) by making use of newly defined factorial difference characters.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.011
      Issue No: Vol. 70 (2018)
       
  • Characters of independent Stanley sequences
    • Authors: Richard A. Moy; Mehtaab Sawhney; David Stoner
      Pages: 354 - 363
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Richard A. Moy, Mehtaab Sawhney, David Stoner
      Odlyzko and Stanley introduced a greedy algorithm for constructing infinite sequences with no 3-term arithmetic progressions when beginning with a finite set with no 3-term arithmetic progressions. The sequences constructed from this procedure are known as Stanley sequences and appear to have two distinct growth rates which dictate whether the sequences are structured or chaotic. A large subclass of sequences of the former type is independent sequences, which have a self-similar structure. An attribute of interest for independent sequences is the character. In this paper, building on recent progress, we prove that every nonnegative integer λ ∉ { 1 , 3 , 5 , 9 , 11 , 15 } is attainable as the character of an independent Stanley sequence, thus resolving a conjecture of Rolnick.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.008
      Issue No: Vol. 70 (2018)
       
  • Randomly twisted hypercubes
    • Authors: Andrzej Dudek; Xavier Pérez-Giménez; Paweł Prałat; Hao Qi; Douglas West; Xuding Zhu
      Pages: 364 - 373
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Andrzej Dudek, Xavier Pérez-Giménez, Paweł Prałat, Hao Qi, Douglas West, Xuding Zhu
      A twisted hypercube of dimension k is created from two twisted hypercubes of dimension k − 1 by adding a matching joining their vertex sets, with the twisted hypercube of dimension 0 consisting of one vertex and no edges. We generate random twisted hypercube by generating the matchings randomly at each step. We show that, asymptotically almost surely, joining any two vertices in a random twisted hypercube of dimension k there are k internally disjoint paths of length at most k lg k + O k lg 2 k . Since the graph is k -regular with 2 k vertices, the number of paths is optimal and the length is asymptotically optimal.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.013
      Issue No: Vol. 70 (2018)
       
  • Existence of regular unimodular triangulations of dilated empty simplices
    • Authors: Takayuki Hibi; Akihiro Higashitani; Koutarou Yoshida
      Pages: 374 - 383
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Takayuki Hibi, Akihiro Higashitani, Koutarou Yoshida
      Given integers k and m with k ≥ 2 and m ≥ 2 , let P be an empty simplex of dimension ( 2 k − 1 ) whose δ -polynomial is of the form 1 + ( m − 1 ) t k . In the present paper, the necessary and sufficient condition for the k th dilation k P of P to have a regular unimodular triangulation will be presented.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.01.012
      Issue No: Vol. 70 (2018)
       
  • The matroid structure of representative triple sets and triple-closure
           computation
    • Authors: Carsten R. Seemann; Marc Hellmuth
      Pages: 384 - 407
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Carsten R. Seemann, Marc Hellmuth
      The closure cl ( R ) of a consistent set R of triples (rooted binary trees on three leaves) provides essential information about tree-like relations that are shown by any supertree that displays all triples in R . In this contribution, we are concerned with representative triple sets, that is, subsets R ′ of R with cl ( R ′ ) = cl ( R ) . In this case, R ′ still contains all information on the tree structure implied by R , although R ′ might be significantly smaller. We show that representative triple sets that are minimal w.r.t. inclusion form the basis of a matroid. This in turn implies that minimal representative triple sets also have minimum cardinality. In particular, the matroid structure can be used to show that minimum representative triple sets can be computed in polynomial time with a simple greedy approach. For a given triple set R that “identifies” a tree, we provide an exact value for the cardinality of its minimum representative triple sets. In addition, we utilize the latter results to provide a novel and efficient method to compute the closure cl ( R ) of a consistent triple set R that improves the time complexity O ( R L R 4 ) of the currently fastest known method proposed by Bryant and Steel (1995). In particular, if a minimum representative triple set for R is given, it can be shown that the time complexity to compute cl ( R ) can be improved by a factor up to R L R . As it turns out, collections of quartets (unrooted binary trees on four leaves) do not provide a matroid structure, in general.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.013
      Issue No: Vol. 70 (2018)
       
  • New bounds on Simonyi’s conjecture
    • Authors: Daniel
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Daniel Soltész
      We say that a pair ( A , B ) is a recovering pair if A and B are set systems on an n -element ground set, such that for every A , A ′ ∈ A and B , B ′ ∈ B we have ( A ∖ B = A ′ ∖ B ′ implies A = A ′ ) and symmetrically ( B ∖ A = B ′ ∖ A ′ implies B = B ′ ). G. Simonyi conjectured that if ( A , B ) is a recovering pair, then A B ≤ 2 n . For the quantity A B the best known upper bound is 2 . 326 4 n due to Holzman and Körner. In this paper we improve this upper bound to 2 . 281 4 n .

      PubDate: 2018-04-16T00:09:32Z
       
  • Pre-adjunctions and the Ramsey property
    • Authors: Dragan
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Dragan Mašulović
      Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. In this paper we propose a new strategy to show that a class of structures has the Ramsey property. The strategy is based on a relatively simple result in category theory and consists of establishing a pre-adjunction between the category of structures which is known to have the Ramsey property, and the category of structures we are interested in. We demonstrate the applicability of this strategy by providing short proofs of three important well known results: we show the Ramsey property for the category of all finite linearly ordered posets with embeddings, for the category of finite convexly ordered ultrametric spaces with embeddings, and for the category of all finite linearly ordered metric spaces (rational metric spaces) with embeddings.

      PubDate: 2018-04-16T00:09:32Z
       
  • Corrigendum to “A general two-term recurrence and its solution”
           [European J. Combin. 33 (2012) 20–26]
    • Authors: Mark Lancaster; Toufik Mansour; Shashikant Mulay; Mark Shattuck
      Abstract: Publication date: Available online 8 April 2018
      Source:European Journal of Combinatorics
      Author(s): Mark Lancaster, Toufik Mansour, Shashikant Mulay, Mark Shattuck


      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.03.004
       
  • Free monoids and generalized metric spaces
    • Authors: Mustapha Kabil; Maurice Pouzet; Ivo G. Rosenberg
      Abstract: Publication date: Available online 2 April 2018
      Source:European Journal of Combinatorics
      Author(s): Mustapha Kabil, Maurice Pouzet, Ivo G. Rosenberg
      Let A be an ordered alphabet, A ∗ be the free monoid over A ordered by the Higman ordering, and let F ( A ∗ ) be the set of final segments of A ∗ . With the operation of concatenation, this set is a monoid. We show that the submonoid F ∘ ( A ∗ ) ≔ F ( A ∗ ) ∖ { ∅ } is free. The MacNeille completion N ( A ∗ ) of A ∗ is a submonoid of F ( A ∗ ) . As a corollary, we obtain that the monoid N ∘ ( A ∗ ) ≔ N ( A ∗ ) ∖ { ∅ } is free. We give an interpretation of the freeness of F ∘ ( A ∗ ) in the category of metric spaces over the Heyting algebra V ≔ F ( A ∗ ) , with the non-expansive mappings as morphisms. Each final segment F of A ∗ yields the injective envelope S F of a two-element metric space over V . The uniqueness of the decomposition of F is due to the uniqueness of the block decomposition of the graph G F associated to this injective envelope.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.008
       
  • 1-well-covered graphs revisited
    • Authors: Vadim E. Levit; Eugen Mandrescu
      Abstract: Publication date: Available online 17 March 2018
      Source:European Journal of Combinatorics
      Author(s): Vadim E. Levit, Eugen Mandrescu
      A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A well-covered graph is 1-well-covered if the deletion of any one vertex leaves a graph, which is well-covered as well (Staples, 1975). A graph G belongs to class W n if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W 1 is the family of all well-covered graphs. It turns out that G ∈ W 2 if and only if it is a 1-well-covered graph without isolated vertices. We show that deleting a shedding vertex does not change the maximum size of a maximal independent set including a given independent set. Specifically, for well-covered graphs, it means that the vertex v is shedding if and only if G − v is well-covered. In addition, we provide new characterizations of 1-well-covered graphs.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.021
       
  • Covering aspects of the Niemeier lattices
    • Authors: Adel Alahmadi; Michel Deza; Mathieu Dutour Sikirić; Patrick Solé
      Abstract: Publication date: Available online 17 March 2018
      Source:European Journal of Combinatorics
      Author(s): Adel Alahmadi, Michel Deza, Mathieu Dutour Sikirić, Patrick Solé
      The Niemeier lattices are the 23 unimodular even lattices of norm 2 in dimension 24. We determine computationally their covering radius for 16 of those lattices and give lower bounds for the remaining that we conjecture to be exact. This is achieved by computing the list of Delaunay polytopes of those lattices.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.038
       
  • Unfoldings of an envelope
    • Authors: Jin Akiyama; Kiyoko Matsunaga
      Abstract: Publication date: Available online 10 March 2018
      Source:European Journal of Combinatorics
      Author(s): Jin Akiyama, Kiyoko Matsunaga
      An envelope is equivalent to a rectangle dihedron or a doubly-covered rectangle. It is cut along a tree graph that spans the four corners of the envelope to get a planar region. We show in Theorem 1 that every region satisfies the Conway criterion and so copies of the region tile the plane using only translations and 180° rotations. Let P 1 and P 2 be two regions obtained by unfolding the same envelope along two non-crossing trees, respectively. Then we show in Theorem 2 that P 1 is equi-rotational into P 2 , which means that P 1 can be dissected into pieces that are hinged at corners, so that the pieces can be rigidly transformed into P 2 by monotonous rotations at the hinges. In Theorems 3 and 4, we give the sufficient conditions for Conway tiles to be foldable into envelopes.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.023
       
  • Metric aggregation functions revisited
    • Authors: Gaspar Mayor; Oscar Valero
      Abstract: Publication date: Available online 9 March 2018
      Source:European Journal of Combinatorics
      Author(s): Gaspar Mayor, Oscar Valero
      In 1981, J. Borsík and J. Doboš analyzed what properties a function must satisfy in order to merge a collection of metric spaces into a single one. Later on, E. Castiñeira, A. Pradera and E. Trillas studied a variant of the same problem in which each metric of the collection to be merged is defined on the same non-empty set. In this, paper we continue the work in this last aforesaid direction. On the one hand, we provide a new characterization of such functions and a few methods to construct them. On the other hand, we analyze the existence of absorbent, idempotent and neutral elements for such class of functions and, thus, we design techniques that allow to discard those functions that are not useful for merging metrics. Finally, we discuss when the functions under study preserve metrics.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.037
       
  • The Sylvester graph and Moore graphs
    • Authors: Vidali
      Abstract: Publication date: Available online 5 March 2018
      Source:European Journal of Combinatorics
      Author(s): A. Jurišić, J. Vidali
      The combinatorial structure of a famous graph with large girth, namely the Sylvester graph, is studied. Simple techniques, such as two-way counting, partitions, circuit chasing and covers are used to identify smaller structures and to show that there are no other graphs that share a small number of regularity properties with it. As a consequence, we show the same for the Hoffman–Singleton graph. We notice that some much larger graphs with large girth have similar properties, and could be studied using the same techniques. In particular, we show that just as the Hoffman–Singleton graph contains the Sylvester graph, a Moore graph of valency 57, whose existence is a famous open problem, must contain a subgraph with a structure that is similar to the one we derived for the Sylvester graph.

      PubDate: 2018-04-16T00:09:32Z
       
  • Channel metrization
    • Authors: Rafael G.L. D’Oliveira; Marcelo Firer
      Abstract: Publication date: Available online 5 March 2018
      Source:European Journal of Combinatorics
      Author(s): Rafael G.L. D’Oliveira, Marcelo Firer
      We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder. We also show that any metric, up to a decoding equivalence, can be isometrically embedded into the hypercube with the Hamming metric, and thus, in terms of decoding, the Hamming metric is universal.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.026
       
  • Regular t-bonded systems in R3
    • Authors: N. Dolbilin; M. Bouniaev
      Abstract: Publication date: Available online 5 March 2018
      Source:European Journal of Combinatorics
      Author(s): N. Dolbilin, M. Bouniaev
      The concept of t -bonded sets is a generalization of the concept of Delone ( r ; R ) -system and a good instrument to create a point set model to describe materials like zeolites, which atomic structures are multi-regular “microporous” point sets. To better describe “microporous” structures it is worthwhile to take into consideration a parameter that represents atomic bonds within the matter. In this paper we generalize for t -bonded systems in R 3 results of the local theory for regular point systems previously proven for Delone ( r , R ) -systems in R 3 . Applying similar concepts and techniques the corresponding results that are proven for multi-regular ( r , R ) -systems could also be generalized for multi-regular t -bonded systems.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.005
       
  • On 2-walk-regular graphs with a large intersection number c2
    • Authors: Zhi Qiao; Jongyook Park; Jack H. Koolen
      Abstract: Publication date: Available online 5 March 2018
      Source:European Journal of Combinatorics
      Author(s): Zhi Qiao, Jongyook Park, Jack H. Koolen
      For a connected amply regular graph with parameters ( v , k , λ , μ ) satisfying λ ≤ μ , it is known that its diameter is bounded by k . This was generalized by Terwilliger to ( s , c , a , k ) -graphs satisfying c ≥ max { a , 2 } . It follows from Terwilliger that a connected amply regular graph with parameters ( v , k , λ , μ ) satisfying μ > k 3 ≥ 1 and μ ≥ λ has diameter at most 7. In this paper we will classify the 2-walk-regular graphs with valency k ≥ 3 and diameter at least 4 such that its intersection number c 2 satisfies c 2 > k 3 . This result generalizes a result of Koolen and Park for distance-regular graphs. And we show that if such a 2-walk-regular graph is not distance-regular, then it is the incidence graph of a group divisible design with the dual property with parameters ( 2 , m ; k ; 0 , λ 2 ) .

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.028
       
  • One combinatorial construction in representation theory
    • Authors: Dmitry Malinin
      Abstract: Publication date: Available online 2 March 2018
      Source:European Journal of Combinatorics
      Author(s): Dmitry Malinin
      Let K be an extension of the field Q p of p -adic rationals, let O K be its ring of integers, and let G be a finite group. According to the classical Jordan–Zassenhaus Theorem, if K ∕ Q p is finite, every isomorphism class of K G -representation modules splits in a finite number of isomorphism classes of O K G -representation modules. We consider a p -group G of a given nilpotency class k > 1 and the extension K ∕ Q p where K = Q p ( ζ p ∞ ) obtained by adjoining all roots ζ p i , i = 1 , 2 , 3 , . . . of unity, and we use an explicit combinatorial construction of a faithful absolutely irreducible K G -module M to show that the number of O K G -isomorphism classes of O K G -representation modules, which are K G -equivalent to M , is infinite, and there are extra congruence properties for these O K G -modules.

      PubDate: 2018-04-16T00:09:32Z
      DOI: 10.1016/j.ejc.2018.02.007
       
  • Binomial edge ideals of bipartite graphs
    • Authors: Davide Bolognini; Antonio Macchia; Francesco Strazzanti
      Pages: 1 - 25
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Davide Bolognini, Antonio Macchia, Francesco Strazzanti
      Binomial edge ideals are a noteworthy class of binomial ideals that can be associated with graphs, generalizing the ideals of 2-minors. For bipartite graphs we prove the converse of Hartshorne’s Connectedness Theorem, according to which if an ideal is Cohen–Macaulay, then its dual graph is connected. This allows us to classify Cohen–Macaulay binomial edge ideals of bipartite graphs, giving an explicit and recursive construction in graph-theoretical terms. This result represents a binomial analogue of the celebrated characterization of (monomial) edge ideals of bipartite graphs due to Herzog and Hibi (2005).

      PubDate: 2017-12-26T18:10:18Z
      DOI: 10.1016/j.ejc.2017.11.004
      Issue No: Vol. 70 (2017)
       
  • Asymptotics of the number of standard Young tableaux of skew shape
    • Authors: Alejandro H. Morales; Igor Pak; Greta Panova
      Pages: 26 - 49
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): Alejandro H. Morales, Igor Pak, Greta Panova
      We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse’s hook-length formula. We also compare our bounds with the existing bounds on the numbers of linear extensions of the corresponding posets.

      PubDate: 2017-12-26T18:10:18Z
      DOI: 10.1016/j.ejc.2017.11.007
      Issue No: Vol. 70 (2017)
       
  • On the degree of regularity of a certain quadratic Diophantine equation
    • Authors: S.D. Adhikari; L. Boza; S. Eliahou; M.P. Revuelta; M.I. Sanz
      Pages: 50 - 60
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): S.D. Adhikari, L. Boza, S. Eliahou, M.P. Revuelta, M.I. Sanz
      We show that, for every positive integer r , there exists an integer b = b ( r ) such that the 4-variable quadratic Diophantine equation ( x 1 − y 1 ) ( x 2 − y 2 ) = b is r -regular. Our proof uses Szemerédi’s theorem on arithmetic progressions.

      PubDate: 2017-12-26T18:10:18Z
      DOI: 10.1016/j.ejc.2017.11.008
      Issue No: Vol. 70 (2017)
       
  • On subgraphs of random Cayley sum graphs
    • Authors: S.V. Konyagin; I.D. Shkredov
      Pages: 61 - 74
      Abstract: Publication date: May 2018
      Source:European Journal of Combinatorics, Volume 70
      Author(s): S.V. Konyagin, I.D. Shkredov
      We prove that asymptotically almost surely, the random Cayley sum graph over a finite abelian group G has edge density close to the expected one on every induced subgraph of size at least log c G , for any fixed c > 1 and G large enough.

      PubDate: 2017-12-26T18:10:18Z
      DOI: 10.1016/j.ejc.2017.11.009
      Issue No: Vol. 70 (2017)
       
 
 
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