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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
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    - MATHEMATICS (651 journals)
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MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
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: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
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 Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
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: 7)
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: 3)
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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
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)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access  
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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 the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
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  
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: 2)
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: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
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: 9)
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: 4)
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: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Discrete Mathematics
  [SJR: 1]   [H-I: 55]   [7 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0012-365X
   Published by Elsevier Homepage  [3043 journals]
  • New 3-designs and 2-designs having U(3,3) as an automorphism group
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Dean Crnković, Vedrana Mikulić Crnković, Andrea Švob
      In this paper we classify 2 -designs and 3 -designs with 28 or 36 points admitting a transitive action of the unitary group U ( 3 , 3 ) on points and blocks. We also construct 2 -designs and 3 -designs with 56 or 63 points and strongly regular graphs on 36, 63 or 126 vertices having U ( 3 , 3 ) as a transitive automorphism group. Further, we show that this completes the classification of 3 -designs admitting a transitive action of the group U ( 3 , 3 ) , in terms of parameters. A number of the 3 -designs and 2 -designs obtained in this paper have not been known before up to our best knowledge.

      PubDate: 2017-07-20T18:30:15Z
       
  • Quantitative (p,q) theorems in combinatorial geometry
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): David Rolnick, Pablo Soberón
      We show quantitative versions of classical results in discrete geometry, where the size of a convex set is determined by some non-negative function. We give versions of this kind for the selection theorem of Bárány, the existence of weak epsilon-nets for convex sets and the ( p , q ) theorem of Alon and Kleitman. These methods can be applied to functions such as the volume, surface area or number of points of a discrete set. We also give general quantitative versions of the colorful Helly theorem for continuous functions.

      PubDate: 2017-07-20T18:30:15Z
       
  • Maximum average degree and relaxed coloring
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Michael Kopreski, Gexin Yu
      We say a graph is ( d , d , … , d , 0 , … , 0 ) -colorable with a of d ’s and b of 0 ’s if V ( G ) may be partitioned into b independent sets O 1 , O 2 , … , O b and a sets D 1 , D 2 , … , D a whose induced graphs have maximum degree at most d . The maximum average degree, m a d ( G ) , of a graph G is the maximum average degree over all subgraphs of G . In this note, for nonnegative integers a , b , we show that if m a d ( G ) < 4 3 a + b , then G is ( 1 1 , 1 2 , … , 1 a , 0 1 , … , 0 b ) -colorable.

      PubDate: 2017-07-20T18:30:15Z
       
  • On some new difference systems of sets constructed from the cyclotomic
           classes of order 12
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Minglong Qi, Shengwu Xiong, Jingling Yuan, Wenbi Rao, Luo Zhong
      Difference system of sets (DSS), introduced by Levenshtein, has an interesting connection with the construction of comma-free codes. In this paper, we construct two new families of DSS from the cyclotomic classes of order 12.

      PubDate: 2017-07-20T18:30:15Z
       
  • Injective choosability of subcubic planar graphs with girth 6
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Boris Brimkov, Jennifer Edmond, Robert Lazar, Bernard Lidický, Kacy Messerschmidt, Shanise Walker
      An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor have distinct colors. A graph G is injectively k -choosable if for any list assignment L , where L ( v ) ≥ k for all v ∈ V ( G ) , G has an injective L -coloring. Injective colorings have applications in the theory of error-correcting codes and are closely related to other notions of colorability. In this paper, we show that subcubic planar graphs with girth at least 6 are injectively 5-choosable. This strengthens the result of Lužar, Škrekovski, and Tancer that subcubic planar graphs with girth at least 7 are injectively 5-colorable. Our result also improves several other results in particular cases.

      PubDate: 2017-07-20T18:30:15Z
       
  • The pure descent statistic on permutations
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Jean-Luc Baril, Sergey Kirgizov
      We introduce a new statistic based on permutation descents which has a distribution given by the Stirling numbers of the first kind, i.e., with the same distribution as for the number of cycles in permutations. We study this statistic on the sets of permutations avoiding one pattern of length three by giving bivariate generating functions. As a consequence, new classes of permutations enumerated by the Motzkin numbers are obtained. Finally, we deduce results about the popularity of the pure descents in all these restricted sets.

      PubDate: 2017-07-20T18:30:15Z
       
  • The extended 1-perfect trades in small hypercubes
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Denis S. Krotov
      An extended 1 -perfect trade is a pair ( T 0 , T 1 ) of two disjoint binary distance- 4 even-weight codes such that the set of words at distance 1 from T 0 coincides with the set of words at distance 1 from T 1 . Such trade is called primary if any pair of proper subsets of T 0 and T 1 is not a trade. Using a computer-aided approach, we classify nonequivalent primary extended 1 -perfect trades of length 10 , constant-weight extended 1 -perfect trades of length 12 , and Steiner trades derived from them. In particular, all Steiner trades with parameters ( 5 , 6 , 12 ) are classified.

      PubDate: 2017-07-20T18:30:15Z
       
  • Vertex-minimal graphs with dihedral symmetry I
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Christina Graves, Stephen J. Graves, L.-K. Lauderdale
      Let D 2 n denote the dihedral group of order 2 n , where n ≥ 3 . In this article, we build upon the findings of Haggard and McCarthy who, for certain values of n , produced a vertex-minimal graph with dihedral symmetry. Specifically, Haggard considered the situation when n 2 or n is a prime power, and McCarthy investigated the case when n is not divisible by 2 , 3 or 5 . In this article, we assume n is not divisible by 4 and construct a vertex-minimal graph whose automorphism group is isomorphic to D 2 n .

      PubDate: 2017-07-20T18:30:15Z
       
  • Limits of structures and the example of tree semi-lattices
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): P. Charbit, L. Hosseini, P. Ossona de Mendez
      The notion of left convergent sequences of graphs introduced by Lovász et al. (in relation with homomorphism densities for fixed patterns and Szemerédi’s regularity lemma) got increasingly studied over the past 10 years. Recently, Nešetřil and Ossona de Mendez introduced a general framework for convergence of sequences of structures. In particular, the authors introduced the notion of Q F -convergence, which is a natural generalization of left-convergence. In this paper, we initiate study of Q F -convergence for structures with functional symbols by focusing on the particular case of tree semi-lattices. We fully characterize the limit objects and give an application to the study of left convergence of m -partite cographs, a generalization of cographs.

      PubDate: 2017-07-20T18:30:15Z
       
  • A generating theorem of simple even triangulations with a finitizable set
           of reductions
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Makoto Nishina, Yusuke Suzuki
      We shall determine exactly two ( P , Q ) -irreducible even triangulations of the projective plane. This result is a new generating theorem of even triangulations of the projective plane, that is, every even triangulation of the projective plane can be obtained from one of those two ( P , Q ) -irreducible even triangulations by a sequence of two expansions called a P -expansion and a Q -expansion, which were used in Batagelj (1984, 1989), Drapal and Lisonek (2010). Furthermore, we prove that for any closed surface F 2 there are finitely many ( P , Q ) -irreducible even triangulations of F 2 .

      PubDate: 2017-07-20T18:30:15Z
       
  • Distinguishing chromatic number of random Cayley graphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Niranjan Balachandran, Sajith Padinhatteeri
      The distinguishing chromatic number of a graph G , denoted χ D ( G ) , is defined as the minimum number of colors needed to properly color G such that no non-trivial automorphism of G fixes each color class of G . In this paper, we consider random Cayley graphs Γ defined over certain abelian groups A with A = n , and show that with probability at least 1 − n − Ω ( log n ) , χ D ( Γ ) ≤ χ ( Γ ) + 1 .

      PubDate: 2017-07-07T17:44:00Z
       
  • The perimeter of words
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour
      We define [ k ] = { 1 , 2 , … , k } to be a (totally ordered) alphabet on k letters. A word w of length n on the alphabet [ k ] is an element of [ k ] n . A word can be represented by a bargraph (i.e., by a column-convex polyomino whose lower edges lie on the x -axis) in which the height of the i th column equals the size of the i th part of the word. Thus these bargraphs have heights which are less than or equal to k . We consider the perimeter, which is the number of edges on the boundary of the bargraph. By way of Cramer’s method and the kernel method, we obtain the generating function that counts the perimeter of words. Using these generating functions we find the average perimeter of words of length n over the alphabet [ k ] . We also show how the mean and variance can be obtained using a direct counting method.

      PubDate: 2017-07-07T17:44:00Z
       
  • Extremal Type II Z4-codes constructed from binary doubly even
           self-dual codes of length 40
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Masaaki Harada
      In this note, we demonstrate that every binary doubly even self-dual code of length 40 can be realized as the residue code of some extremal Type II Z 4 -code. As a consequence, it is shown that there are at least 94356 inequivalent extremal Type II Z 4 -codes of length 40 .

      PubDate: 2017-07-07T17:44:00Z
       
  • The covering radius of PGL2(q)
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Binzhou Xia
      The covering radius of a subset C of the symmetric group S n is the maximal Hamming distance of an element of S n from C . This note determines the covering radii of the finite 2 -dimensional projective general linear groups. It turns out that the covering radius of PGL 2 ( q ) is q − 2 if q is even, and is q − 3 if q is odd.

      PubDate: 2017-07-07T17:44:00Z
       
  • Toll number of the Cartesian and the lexicographic product of graphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Tanja Gologranc, Polona Repolusk
      Toll convexity is a variation of the so-called interval convexity. A tolled walk T between two non-adjacent vertices u and v in a graph G is a walk, in which u is adjacent only to the second vertex of T and v is adjacent only to the second-to-last vertex of T . A toll interval between u , v ∈ V ( G ) is a set T G ( u , v ) = { x ∈ V ( G ) : x  lies on a tolled walk between  u  and  v } . A set S ⊆ V ( G ) is toll convex, if T G ( u , v ) ⊆ S for all u , v ∈ S . A toll closure of a set S ⊆ V ( G ) is the union of toll intervals between all pairs of vertices from S . The size of a smallest set S whose toll closure is the whole vertex set is called a toll number of a graph G , t n ( G ) . The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if H is not isomorphic to a complete graph, t n ( G ∘ H ) ≤ 3 ⋅ t n ( G ) . We give some necessary and sufficient conditions for t n ( G ∘ H ) = 3 ⋅ t n ( G ) . Moreover, if G has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with t n ( G ∘ H ) = 2 are characterized. Finally, the formula for t n ( G ∘ H ) is given — it is described in terms of the so-called toll-dominating triples or, if H is complete, toll-dominating pairs.

      PubDate: 2017-07-07T17:44:00Z
       
  • Perfect f-matchings and f-factors in hypergraphs—A combinatorial
           approach
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Isabel Beckenbach, Robert Scheidweiler
      We prove characterizations of the existence of perfect f -matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f -factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the f -factor problem is NP -hard.

      PubDate: 2017-07-07T17:44:00Z
       
  • Graphs and their associated inverse semigroups
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Tien Chih, Demitri Plessas
      Directed graphs have long been used to gain an understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in a characterization theorem and an analog of Frucht’s Theorem. We investigate two inverse semigroups defined over undirected graphs constructed from the notions of subgraph and vertex set induced subgraph. We characterize the structure of the semilattice of idempotents and lattice of ideals of these inverse semigroups. We prove a characterization theorem that states that every graph has a unique associated inverse semigroup up to isomorphism allowing for an algebraic restatement of the Edge Reconstruction Conjecture.

      PubDate: 2017-06-26T17:13:31Z
       
  • Infinite families of 2-designs and 3-designs from linear codes
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Cunsheng Ding, Chengju Li
      The interplay between coding theory and t -designs started many years ago. While every t -design yields a linear code over every finite field, the largest t for which an infinite family of t -designs is derived directly from a linear or nonlinear code is t = 3 . Sporadic 4 -designs and 5 -designs were derived from some linear codes of certain parameters. The major objective of this paper is to construct many infinite families of 2 -designs and 3 -designs from linear codes. The parameters of some known t -designs are also derived. In addition, many conjectured infinite families of 2 -designs are also presented.

      PubDate: 2017-06-26T17:13:31Z
       
  • Large butterfly Cayley graphs and digraphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): David Bevan
      We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large  k and for values of  d taken from a large interval, the largest known Cayley graphs and digraphs of diameter  k and degree  d . Another method yields, for sufficiently large  k and infinitely many values of  d , Cayley graphs and digraphs of diameter  k and degree  d whose order is exponentially larger in  k than any previously constructed. In the directed case, these are within a linear factor in k of the Moore bound.

      PubDate: 2017-06-26T17:13:31Z
       
  • Centralizer algebras of the group associated to Z4-codes
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Masashi Kosuda, Manabu Oura
      The purpose of this paper is to investigate the finite group which appears in the study of the Type II Z 4 -codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer algebras of the tensor representations of this group.

      PubDate: 2017-06-26T17:13:31Z
       
  • Bounded clique cover of some sparse graphs
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Andrea Munaro
      We show that f ( x ) = ⌊ 3 2 x ⌋ is a θ -bounding function for the class of subcubic graphs and that it is best possible. This generalizes a result by Henning et al. (2012), who showed that θ ( G ) ≤ 3 2 α ( G ) for any subcubic triangle-free graph G . Moreover, we provide a θ -bounding function for the class of K 4 -free graphs with maximum degree at most 4 . Finally, we study the problem Clique Cover for subclasses of planar graphs and graphs with bounded maximum degree: in particular, answering a question of Cerioli et al. (2008), we show it admits a PTAS for planar graphs.

      PubDate: 2017-06-26T17:13:31Z
       
  • Chromatic number via Turán number
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Meysam Alishahi, Hossein Hajiabolhassan
      For a graph G and a family of graphs F , the general Kneser graph KG ( G , F ) is a graph with the vertex set consisting of all subgraphs of G isomorphic to some member of F and two vertices are adjacent if their corresponding subgraphs are edge disjoint. In this paper, we introduce some generalizations of Turán number of graphs. In view of these generalizations, we give some lower and upper bounds for the chromatic number of general Kneser graphs KG ( G , F ) . Using these bounds, we determine the chromatic number of some family of general Kneser graphs KG ( G , F ) in terms of generalized Turán number of graphs. In particular, we determine the chromatic number of every Kneser multigraph KG ( G , F ) where G is a multigraph each of whose edges has the multiplicity at least 2 and F is an arbitrary family of simple graphs. Moreover, the chromatic number of general Kneser graph KG ( G , F ) is exactly determined where G is a dense graph and F = { K 1 , 2 } .

      PubDate: 2017-06-19T16:00:47Z
       
  • Sums of powers of Catalan triangle numbers
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Pedro J. Miana, Hideyuki Ohtsuka, Natalia Romero
      In this paper, we consider combinatorial numbers ( C m , k ) m ≥ 1 , k ≥ 0 , mentioned as Catalan triangle numbers where C m , k ≔ m − 1 k − m − 1 k − 1 . These numbers unify the entries of the Catalan triangles B n , k and A n , k for appropriate values of parameters m and k , i.e.,  B n , k = C 2 n , n − k and A n , k = C 2 n + 1 , n + 1 − k . In fact, these numbers are suitable rearrangements of the known ballot numbers and some of these numbers are the well-known Catalan numbers C n that is C 2 n , n − 1 = C 2 n + 1 , n = C n . We present identities for sums (and alternating sums) of C m , k , squares and cubes of C m , k and, consequently, for B n , k and A n , k . In particular, one of these identities solves an open problem posed in Gutiérrez et al. (2008). We also give some identities between ( C m , k ) m ≥ 1 , k ≥ 0 and harmonic numbers ( H n ) n ≥ 1 . Finally, in the last section, new open problems and identities involving ( C n ) n ≥ 0 are conjectured.

      PubDate: 2017-06-19T16:00:47Z
       
  • Hexavalent symmetric graphs of order 9p
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Song-Tao Guo, Hailong Hou, Yong Xu
      A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify hexavalent symmetric graphs of order 9 p for each prime p .

      PubDate: 2017-06-19T16:00:47Z
       
  • Improving the Clark–Suen bound on the domination number of the
           Cartesian product of graphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Boštjan Brešar
      A long-standing Vizing’s conjecture asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers; one of the most significant results related to the conjecture is the bound of Clark and Suen, γ ( G □ H ) ≥ γ ( G ) γ ( H ) ∕ 2 , where γ stands for the domination number, and G □ H is the Cartesian product of graphs G and H . In this note, we improve this bound by employing the 2-packing number ρ ( G ) of a graph G into the formula, asserting that γ ( G □ H ) ≥ ( 2 γ ( G ) − ρ ( G ) ) γ ( H ) ∕ 3 . The resulting bound is better than that of Clark and Suen whenever G is a graph with ρ ( G ) < γ ( G ) ∕ 2 , and in the case G has diameter 2 reads as γ ( G □ H ) ≥ ( 2 γ ( G ) − 1 ) γ ( H ) ∕ 3 .

      PubDate: 2017-06-19T16:00:47Z
       
  • Distant sum distinguishing index of graphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Jakub Przybyło
      Consider a positive integer r and a graph G = ( V , E ) with maximum degree Δ and without isolated edges. The least k so that a proper edge colouring c : E → { 1 , 2 , … , k } exists such that ∑ e ∋ u c ( e ) ≠ ∑ e ∋ v c ( e ) for every pair of distinct vertices u , v at distance at most r in G is denoted by χ Σ , r ′ ( G ) . For r = 1 , it has been proved that χ Σ , 1 ′ ( G ) = ( 1 + o ( 1 ) ) Δ . For any r ≥ 2 in turn an infinite family of graphs is known with χ Σ , r ′ ( G ) = Ω ( Δ r − 1 ) . We prove that, on the other hand, χ Σ , r ′ ( G ) = O ( Δ r − 1 ) for r ≥ 2 . In particular, we show that χ Σ , r ′ ( G ) ≤ 6 Δ r − 1 if r ≥ 4 .

      PubDate: 2017-06-19T16:00:47Z
       
  • Set systems with positive intersection sizes
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Jiuqiang Liu, Xiaodong Liu
      In this paper, we derive a best possible k -wise extension to the well-known Snevily theorem on set systems (Snevily, 2003) which strengthens the well-known theorem by Füredi and Sudakov (2004). We also provide a conjecture which gives a common generalization to all existing non-modular L -intersection theorems.

      PubDate: 2017-06-14T15:30:45Z
       
  • 3-Restricted arc connectivity of digraphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Shangwei Lin, Ya’nan Jin, Chunfang Li
      The k -restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset S of a strong digraph D is a k -restricted arc cut if D − S has a strong component D ′ with order at least k such that D − V ( D ′ ) contains a connected subdigraph with order at least k . The k -restricted arc connectivity λ k ( D ) of a digraph D is the minimum cardinality over all k -restricted arc cuts of D . Let D be a strong digraph with order n ≥ 6 and minimum degree δ ( D ) . In this paper, we first show that λ 3 ( D ) exists if δ ( D ) ≥ 3 and, furthermore, λ 3 ( D ) ≤ ξ 3 ( D ) if δ ( D ) ≥ 4 , where ξ 3 ( D ) is the minimum 3-degree of D . Next, we prove that λ 3 ( D ) = ξ 3 ( D ) if δ ( D ) ≥ n + 3 2 . Finally, we give examples showing that these results are best possible in some sense.

      PubDate: 2017-06-14T15:30:45Z
       
  • A note on fractional disjoint transversals in hypergraphs
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Michael A. Henning, Anders Yeo
      A transversal in a hypergraph H is a subset of vertices that has a nonempty intersection with every edge of H . A transversal family F of H is a family of (not necessarily distinct) transversals of H . The effective transversal-ratio of the family F is the ratio of the number of sets in F over the maximum times  r F any element appears in  F . The fractional disjoint transversal number FDT ( H ) is the supremum of the effective transversal-ratio taken over all transversal families. That is, FDT ( H ) = sup F F ∕ r F . Using a connection with not-all-equal 3 -SAT, we prove that if H is a 3 -regular 3 -uniform hypergraph, then FDT ( H ) ≥ 2 , which proves a known conjecture. Using probabilistic arguments, we prove that for all k ≥ 3 , if H is a k -regular k -uniform hypergraph, then FDT ( H ) ≥ 1 ∕ ( 1 − ( k − 1 k ) 1 k 1 k − 1 ) , and that this bound is essentially best possible.

      PubDate: 2017-06-14T15:30:45Z
       
  • A divide-and-conquer bound for aggregate’s quality and algebraic
           connectivity
    • Abstract: Publication date: October 2017
      Source:Discrete Mathematics, Volume 340, Issue 10
      Author(s): Artem Napov
      We establish a divide-and-conquer bound for the aggregate’s quality and algebraic connectivity measures, as defined for weighted undirected graphs. Aggregate’s quality is defined on a set of vertices and, in the context of aggregation-based multigrid methods, it measures how well this set of vertices is represented by a single vertex. On the other hand, algebraic connectivity is defined on a graph, and measures how well this graph is connected. The considered divide-and-conquer bound for aggregate’s quality relates the aggregate’s quality of a union of two disjoint sets of vertices to the aggregate’s quality of the two sets. Likewise, the bound for algebraic connectivity relates the algebraic connectivity of the graph induced by a union of two disjoint sets of vertices to the algebraic connectivity of the graphs induced by the two sets.

      PubDate: 2017-06-14T15:30:45Z
       
  • Repeated-root constacyclic codes of length nlps
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Li Liu, Lanqiang Li, Liqi Wang, Shixin Zhu
      In this paper, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length n l p s over F q and their dual codes, where l is an odd prime different from p , and n is an odd prime different from both l and p such that n = 2 h + 1 for some prime h or h = 1 . Moreover, we give all self-dual cyclic codes of length n l p s over F q and their enumeration. All linear complementary dual (LCD) cyclic codes of length n l p s over F q and their enumeration are also obtained.

      PubDate: 2017-05-25T13:58:21Z
       
  • Some more uniformly resolvable designs with block sizes 2 and 4
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Hengjia Wei, Gennian Ge
      A uniformly resolvable design (URD) is a resolvable design in which each parallel class contains blocks of only one block size k . Such a class is denoted k -pc and for a given k the number of k -pcs is denoted r k . The number of points of the URD is denoted by v . In the literature, the existence of URDs of block sizes k 1 and k 2 with { k 1 , k 2 } ∈ { { 2 , 3 } , { 2 , 4 } , { 3 , 4 } } has been studied with much efforts. For { k 1 , k 2 } = { 2 , 3 } or { 3 , 4 } , the existence spectra have been determined completely, while for { k 1 , k 2 } = { 2 , 4 } there are still 1338 undetermined pairs of ( v , r 2 ) . In this paper we continue the study on the existence of URDs of block sizes 2 and 4. We improve the known results by reducing the number of open cases from 1338 to 16 . In addition, we prove that there exist 4 -RGDDs of types 2178, 2250 and 2334.

      PubDate: 2017-05-25T13:58:21Z
       
  • On symmetric graphs of order four times an odd square-free integer and
           valency seven
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Jiangmin Pan, Bo Ling, Suyun Ding
      A graph is called symmetric if its automorphism group is transitive on its arcs. In this paper, we classify symmetric graphs of order four times an odd square-free integer and valency seven. It is shown that, either the graph is isomorphic to one of 9 specific graphs or its full automorphism group is isomorphic to PSL ( 2 , p ) , PGL ( 2 , p ) , PSL ( 2 , p ) × Z 2 or PGL ( 2 , p ) × Z 2 with p ≡ ± 1 ( mod 7 ) a prime.

      PubDate: 2017-05-20T13:48:31Z
       
  • Exponentially many graphs have a Q-cospectral mate
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): João Carvalho, Bruna S. Souza, Vilmar Trevisan, Fernando C. Tura
      We develop an algorithm for computing the characteristic polynomial of matrices related to threshold graphs. We use this as tool to exhibit, for any natural number n ≥ 4 , 2 n − 4 graphs with n vertices that have a non isomorphic pair with the same signless Laplacian spectrum. We also show how to construct infinite families of pairs of non isomorphic graphs having the same Q -spectrum.

      PubDate: 2017-05-20T13:48:31Z
       
  • A new characterization of equipartite graphs
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): M.H. Shirdareh Haghighi, F. Motialah, B. Amini
      A graph G of order 2 n is called equipartite if for every n -element set A ⊆ V ( G ) , there exists an automorphism of G that maps the induced subgraph G [ A ] onto G [ V ( G ) ∖ A ] . In this paper, we show that a graph G of order 2 n is equipartite if and only if for every such partition of V ( G ) , the induced subgraphs G [ A ] and G [ V ( G ) ∖ A ] have the same Laplacian spectra.

      PubDate: 2017-05-20T13:48:31Z
       
  • Enumerations of vertices among all rooted ordered trees with levels and
           degrees
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Sen-Peng Eu, Seunghyun Seo, Heesung Shin
      In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ , (ii) non-first-children of degree k at level ℓ − 1 , (iii) leaves having k − 1 elder siblings at level ℓ , and (iv) non-leaves of outdegree k at level ℓ − 1 . Our results unite and generalize several previous works in the literature.

      PubDate: 2017-05-20T13:48:31Z
       
  • Every planar graph without cycles of length 4 or 9 is (1,1,0)-colorable
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Lifeng Dai, Yingqian Wang, Jinghan Xu
      Let d 1 , d 2 , … , d k be k non-negative integers. A graph G is ( d 1 , d 2 , … , d k ) -colorable, if the vertex set of G can be partitioned into subsets V 1 , V 2 , … , V k such that the subgraph G [ V i ] induced by V i has maximum degree at most d i for i = 1 , 2 , … , k . In this paper, we prove that every planar graph without cycles of length 4 or 9 is ( 1 , 1 , 0 ) -colorable.

      PubDate: 2017-05-20T13:48:31Z
       
  • Edge-colorings of graphs avoiding complete graphs with a prescribed
           coloring
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Fabrício S. Benevides, Carlos Hoppen, Rudini M. Sampaio
      Given a graph F and an integer r ≥ 2 , a partition F ̂ of the edge set of F into at most r classes, and a graph G , define c r , F ̂ ( G ) as the number of r -colorings of the edges of G that do not contain a copy of F such that the edge partition induced by the coloring is isomorphic to the one of F . We think of F ̂ as the pattern of coloring that should be avoided. The main question is, for a large enough n , to find the (extremal) graph G on n vertices which maximizes c r , F ̂ ( G ) . This problem generalizes a question of Erdős and Rothschild, who originally asked about the number of colorings not containing a monochromatic clique (which is equivalent to the case where F is a clique and the partition F ̂ contains a single class). We use Hölder’s Inequality together with Zykov’s Symmetrization to prove that, for any r ≥ 2 , k ≥ 3 and any pattern K k ̂ of the clique K k , there exists a complete multipartite graph that is extremal. Furthermore, if the pattern K k ̂ has at least two classes, with the possible exception of two very small patterns (on three or four vertices), every extremal graph must be a complete multipartite graph. In the case that r = 3 and F ̂ is a rainbow triangle (that is, where F = K 3 and each part is a singleton), we show that an extremal graph must be an almost complete graph. Still for r = 3 , we extend a result about monochromatic patterns of Alon, Balogh, Keevash and Sudakov to some patterns that use two of the three colors, finding the exact extremal graph. For the later two results, we use the Regularity and Stability Method.

      PubDate: 2017-05-20T13:48:31Z
       
  • Non-existence of two types of partial difference sets
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Stefaan De Winter, Eric Neubert, Zeying Wang
      In this note we prove the non-existence of two types of partial difference sets in Abelian groups of order 216 . This completes the classification of parameters for which a partial difference set of size at most 100 exists in an Abelian group.

      PubDate: 2017-05-20T13:48:31Z
       
  • A topological framework for signed permutations
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Fenix W.D. Huang, Christian M. Reidys
      In this paper, we present a topological framework for studying signed permutations and their reversal distance. This framework is based on a presentation of orientable and non-orientable fatgraphs via sectors. As an application, we give an alternative approach and interpretation of the Hannenhalli–Pevzner formula for the reversal distance of sorting signed permutations. This is obtained by constructing a bijection between signed permutations and certain equivalence classes of fatgraphs, called π -maps. We study the action of reversals and show that they either splice, glue or half-flip external vertices, which implies that any reversal changes the topological genus by at most one. We show that the lower bound of the reversal distance of a signed permutation equals the topological genus of its π -maps. We then discuss how the new topological model connects to other sorting problems.

      PubDate: 2017-05-20T13:48:31Z
       
  • Poisson approximation of counts of induced subgraphs in random
           intersection graphs
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Katarzyna Rybarczyk, Dudley Stark
      Random intersection graphs are characterised by three parameters: n , m and p , where n is the number of vertices, m is the number of objects, and p is the probability that a given object is associated with a given vertex. Two vertices in a random intersection graph are adjacent if and only if they have an associated object in common. When m = ⌊ n α ⌋ for constant α , we provide a condition, called strictly α -balanced, for the Poisson convergence of the number of induced copies of a fixed subgraph.

      PubDate: 2017-05-20T13:48:31Z
       
  • A weighted Möbius function
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Derek Garton
      Fix an odd prime ℓ and let G be the poset of isomorphism classes of finite abelian ℓ -groups, ordered by inclusion. If ξ : G → R ≥ 0 is a discrete probability distribution on G and A ∈ G , define the A th moment of ξ to be ∑ B ∈ G Surj ( B , A ) ξ ( B ) . The question of determining conditions that ensure ξ is completely determined by its moments has been of recent interest in many problems of Cohen–Lenstra type. Furthermore, recovering ξ from its moments requires a new Möbius-type inversion formula on G . In this paper, we define this function, relate it to the classical Möbius function on the poset of subgroups of a fixed group, and prove two theorems about when it vanishes. As one corollary of these theorems, we obtain an analog of Hall’s theorem on the vanishing of the classical Möbius function. As another, we obtain an infinite family of pairs of groups on which the classical Möbius function vanishes; obtaining such pairs is a group-theoretic topic of recent interest.

      PubDate: 2017-05-20T13:48:31Z
       
  • Lambert series and conjugacy classes in GL
    • Abstract: Publication date: September 2017
      Source:Discrete Mathematics, Volume 340, Issue 9
      Author(s): Mircea Merca
      A relationship between the general linear group G L ( n , m ) and integer partitions was investigated by Macdonald in order to calculate the number of conjugacy classes in G L ( n , m ) . In this paper, the author introduced two different factorizations for a special case of Lambert series in order to prove that the number of conjugacy classes in the general linear group G L ( n , m ) and the number of partitions of n into k different magnitudes are related by a finite discrete convolution. New identities involving overpartitions, partitions into k different magnitudes and other combinatorial objects are discovered and proved in this context.

      PubDate: 2017-05-20T13:48:31Z
       
 
 
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