Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 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: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
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: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 4)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 21)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 7)
Advances in Materials Science     Open Access   (Followers: 23)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 7)
Algorithms     Open Access   (Followers: 15)
Algorithms Research     Open Access   (Followers: 2)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 17)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 17)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 22)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     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: 5)
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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
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  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 3)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 22)
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: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 12)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 12)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
COMBINATORICA
Journal Prestige (SJR): 1.764
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1439-6912 - ISSN (Online) 0209-9683
Published by Springer-Verlag Homepage  [2467 journals]
  • A Family of Balanced Generalized Weighing Matrices

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      Abstract: Abstract Balanced weighing matrices with parameters $$\left({1 + 18 \cdot {{{9^{m + 1}} - 1} \over 8},{9^{m + 1}},4 \cdot {9^m}} \right),$$ for each nonzero integer m are constructed. This is the first infinite class not belonging to those with classical parameters. It is shown that any balanced weighing matrix is equivalent to a five-class association scheme.
      PubDate: 2022-12-01
       
  • A Short Proof of the Blow-Up Lemma for Approximate Decompositions

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      Abstract: Abstract Kim, Kühn, Osthus and Tyomkyn (Trans. Amer. Math. Soc. 371 (2019), 4655–4742) greatly extended the well-known blow-up lemma of Komlós, Sárközy and Szemerédi by proving a ‘blow-up lemma for approximate decompositions’ which states that multipartite quasirandom graphs can be almost decomposed into any collection of bounded degree graphs with the same multipartite structure and slightly fewer edges. This result has already been used by Joos, Kim, Kühn and Osthus to prove the tree packing conjecture due to Gyárfás and Lehel from 1976 and Ringel’s conjecture from 1963 for bounded degree trees as well as implicitly in the recent resolution of the Oberwolfach problem (asked by Ringel in 1967) by Glock, Joos, Kim, Kühn and Osthus. Here we present a new and significantly shorter proof of the blow-up lemma for approximate decompositions. In fact, we prove a more general theorem that yields packings with stronger quasirandom properties which is useful for potential applications.
      PubDate: 2022-12-01
       
  • Bipartite Turán Problems for Ordered Graphs

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      Abstract: Abstract A zero-one matrix M contains a zero-one matrix A if one can delete some rows and columns of M, and turn some 1-entries into 0-entries such that the resulting matrix is A. The extremal number of A, denoted by ex(n, A), is the maximum number of 1-entries in an n × n sized matrix M that does not contain A. A matrix A is column-t-partite (or row-t-partite), if it can be cut along the columns (or rows) into t submatrices such that every row (or column) of these submatrices contains at most one 1-entry. We prove that if A is column-t-partite, then \({\rm{ex}}(n,A) < {n^{2 - {1 \over t} + {1 \over {{t^2}}} + o(1)}}\) and if A is both column- and row-t-partite, then \({\rm{ex}}(n,A) < {n^{2 - {1 \over t} + o(1)}}\) . Our proof combines a novel density-increment-type argument with the celebrated dependent random choice method. Results about the extremal numbers of zero-one matrices translate into results about the Turán numbers of bipartite ordered graphs. In particular, a zero-one matrix with at most t 1-entries in each row corresponds to a bipartite ordered graph with maximum degree t in one of its vertex classes. Our results are partially motivated by a well-known result of Füredi (1991) and Alon, Krivelevich, Sudakov (2003) stating that if H is a bipartite graph with maximum degree t in one of the vertex classes, then \({\rm{ex}}(n,H) = O({n^{2 - {1 \over t}}})\) . The aim of the present paper is to establish similar general results about the extremal numbers of ordered graphs.
      PubDate: 2022-12-01
       
  • Convergence and Limits of Finite Trees

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      Abstract: Abstract Motivated by the work of Lovász and Szegedy on the convergence and limits of dense graph sequences [10], we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. We introduce dendrons (a notion based on separable real trees) and show that the sampling limits of finite trees are exactly the dendrons. We also prove that the limit dendron is unique.
      PubDate: 2022-12-01
       
  • The Number of Maximal Independent Sets in the Hamming Cube

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      Abstract: Abstract Let Qn be the n-dimensional Hamming cube and N = 2n. We prove that the number of maximal independent sets in Qn is asymptotically $$2n{2^{N/4}},$$ as was conjectured by Ilinca and the first author in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent sets and induced matchings. The proof that it is also an upper bound draws on various tools, among them “stability” results for maximal independent set counts and old and new results on isoperimetric behavior in Qn.
      PubDate: 2022-12-01
       
  • The Sandpile Group of a Trinity and a Canonical Definition for the Planar
           Bernardi Action

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      Abstract: Abstract Baker and Wang define the so-called Bernardi action of the sandpile group of a ribbon graph on the set of its spanning trees. This potentially depends on a fixed vertex of the graph but it is independent of the base vertex if and only if the ribbon structure is planar, moreover, in this case the Bernardi action is compatible with planar duality. Earlier, Chan, Church and Grochow and Chan, Glass, Macauley, Perkinson, Werner and Yang proved analogous results about the rotor-routing action. Baker and Wang moreover showed that the Bernardi and rotor-routing actions coincide for plane graphs. We clarify this still confounding picture by giving a canonical definition for the planar Bernardi/rotor-routing action, and also a canonical description of the isomorphism between sandpile groups of planar dual graphs. Our definition implies the compatibility with planar duality via an extremely short argument. We also uncover hidden symmetries of the problem by proving our results in the slightly more general setting of balanced plane digraphs. Any balanced plane digraph gives rise to a trinity, i.e., a triangulation of the sphere with a three-coloring of the 0-simplices. Our most important tool is a group associated to trinities, introduced by Cavenagh and Wanless, and a result of a subset of the authors characterizing the Bernardi bijection in terms of spanning trees dual to arborescences.
      PubDate: 2022-10-26
      DOI: 10.1007/s00493-021-4798-9
       
  • Constructing Tree-Decompositions That Display All Topological Ends

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      Abstract: Abstract We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4987-1
       
  • On the Chevalley-Warning Theorem When the Degree Equals the Number of
           Variables

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      Abstract: Abstract Let f be a degree d polynomial in n variables defined over a finite field k of characteristic p and let N be the number of zeros of f in kn. The Chevalley-Warning theorem asserts that if d<n, then N is divisible by p. In this note we show a version of the result for d = n.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-5043-x
       
  • Second-Order Bounds on Correlations Between Increasing Families

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      Abstract: Abstract Harris’s correlation inequality states that any two monotone functions on the Boolean hy-percube are positively correlated. Talagrand [11] started a line of works in search of quantitative versions of this fact by providing a lower bound on the correlation in terms of the influences of the functions. A famous conjecture of Chvátal [2] was found by Friedgut, Kahn, Kalai and Keller [5] to be equivalent to a certain strengthening of Talagrand’s bound, conjectured to hold true when one of the functions is antipodal (i.e., g(x) = 1 − g(−x). Motivated by this conjecture, we strengthen some of those bounds by giving estimates that also involve the second order Fourier coefficients of the functions. In particular, we show that the bounds due to Talagrand and due to Keller, Mossel and Sen [8] can be improved when one of the functions is antipodal. Our proofs follow a different route than the ones in the literature, and the analysis is carried out in the Gaussian setting.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-021-4417-9
       
  • Complexity of Branch-and-Bound and Cutting Planes in Mixed-Integer
           Optimization — II

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      Abstract: Abstract We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut framework can be orders of magnitude more efficient than employing these tools on their own. In particular, we give general conditions under which a cutting plane strategy and a branching scheme give a provably exponential advantage in efficiency when combined into branch-and-cut. The efficiency of these algorithms is evaluated using two concrete measures: number of iterations and sparsity of constraints used in the intermediate linear/convex programs. To the best of our knowledge, our results are the first mathematically rigorous demonstration of the superiority of branch-and-cut over pure cutting planes and pure branch-and-bound.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4884-7
       
  • Finding Certain Arithmetic Progressions in 2-Coloured Cyclic Groups

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      Abstract: Abstract We say a pair of integers (a, b) is findable if the following is true. For any δ > 0 there exists a p0 such that for any prime p ≥ p0 and any red-blue colouring of ℤ/pℤ in which each colour has density at least δ, we can find an arithmetic progression of length a + b inside ℤ/pℤ whose first a elements are red and whose last b elements are blue. Szemeredi’s Theorem on arithmetic progressions implies that (0, k) and (1, k) are find-able for any k. We prove that (2, k) is also findable for any k. However, the same is not true of (3, k). Indeed, we give a construction showing that (3,30000) is not findable. We also show that (14, 14) is not findable.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4901-x
       
  • On the Classification of Low-Degree Ovoids of Q(4,q)

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      Abstract: Abstract Ovoids of the non-degenerate quadric Q(4,q) of PG(4,q) have been studied since the end of the’ 80s. They are rare objects and, beside the classical example given by an elliptic quadric, only three classes are known for q odd, one class for q even, and a sporadic example for q = 35. It is well known that to any ovoid of Q(4,q) a bivariate polynomial f (x,y) can be associated. In this paper we classify ovoids of Q(4,q) whose corresponding polynomial f (x, y) has “low degree” compared with q, in particular, \(\deg \left( f \right) < {\left( {{1 \over {6.3}}q} \right)^{{3 \over {13}}}} - 1\) . Finally, as an application, two classes of permutation polynomials in characteristic 3 are obtained.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-5005-3
       
  • Maximal Digraphs with Respect to Primitive Positive Constructability

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      Abstract: Abstract We study the class of all finite directed graphs (digraphs) up to primitive positive constructibility. The resulting order has a unique maximal element, namely the digraph P1 with one vertex and no edges. The digraph P1 has a unique maximal lower bound, namely the digraph P2 with two vertices and one directed edge. Our main result is a complete description of the maximal lower bounds of P2; we call these digraphs submaximal. We show that every digraph that is not equivalent to P1 and P2 is below one of the submaximal digraphs.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4918-1
       
  • Improved Lower Bounds for Van Der Waerden Numbers

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      Abstract: Abstract Recently, Ben Green proved that the two-color van der Waerden number ω(3, k) is bounded from below by \({k^{{b_0}\left( k \right)}}\) where \({b_0}\left( k \right) = {c_0}{\left( {{{\log \,k} \over {\log \log \,k}}} \right)^{1/3}}\) . We prove a new lower bound of kb(k) with \(b\left( k \right) = {{c\log \,k} \over {\log \log \,k}}\) . This is done by modifying Green’s argument, replacing a complicated result about random quadratic forms with an elementary probabilistic result.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4925-2
       
  • Fractionally Balanced Hypergraphs and Rainbow KKM Theorems

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      Abstract: Abstract A d-partite hypergraph is called fractionally balanced if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall’s theorem we prove lower bounds on the matching number of such hypergraphs. These bounds yield rainbow versions of the KKM theorem for products of simplices, which in turn are used to obtain some results on multiple-cake division, and on rainbow matchings in families of d-intervals.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-021-4808-y
       
  • A Generalization of the Graph Packing Theorems of Sauer-Spencer and Brandt

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      Abstract: Abstract We prove a common generalization of the celebrated Sauer-Spencer packing theorem and a theorem of Brandt concerning finding a copy of a tree inside a graph. This proof leads to the characterization of the extremal graphs in the case of Brandt’s theorem: If G is a graph and F is a forest, both on n vertices, and 3Δ(G) + ℓ* (F) ≤ n, then G and F pack unless n is even, \(G = {n \over 2}{K_2}\) and F = K1,n−1 where ℓ*(F) is the difference between the number of leaves and twice the number of nontrivial components of F.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-022-4932-3
       
  • Vertex-Minor-Closed Classes are χ-Bounded

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      Abstract: Abstract We prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is χ-bounded.
      PubDate: 2022-10-10
      DOI: 10.1007/s00493-021-4767-3
       
  • Algebraic Constructions of Complete m-Arcs

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      Abstract: Abstract Let m be a positive integer, q be a prime power, and PG(2,q) be the projective plane over the finite field \({\mathbb{F}_q}\) . Finding complete m-arcs in PG(2,q) of size less than q is a classical problem in finite geometry. In this paper we give a complete answer to this problem when q is relatively large compared with m, explicitly constructing the smallest m-arcs in the literature so far for any m ≥ 8. For any fixed m, our arcs \({{\cal A}_{q,m}}\) satisfy \(\left {{{\cal A}_{q,m}}} \right - q \to - \infty \) as q grows. To produce such m-arcs, we develop a Galois theoretical machinery that allows the transfer of geometric information of points external to the arc, to arithmetic one, which in turn allows to prove the m-completeness of the arc.
      PubDate: 2022-10-01
       
  • Calculating the Euler Characteristic of the Moduli Space of Curves

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      Abstract: Abstract The orbifold Euler characteristic of the moduli space \({{\cal M}_{g;1}}\) of genus g smooth curves with one marked point (g ≥ 1) was calculated by Harer and Zagier: \(\chi ({{\cal M}_{g;1}}) = \zeta (1 - 2g) = - {B_{2g}}/(2g)\) , where ζ is the Riemann zeta function and B2g is the (2g)th Bernoulli number. We give a shorter proof of this result using only formal power series and classical combinatorics.
      PubDate: 2022-10-01
       
  • On the Critical Exponent for k-Primitive Sets

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      Abstract: Abstract A set of positive integers is primitive (or 1-primitive) if no member divides another. Erdős proved in 1935 that the weighted sum ∑1/(n log n) for n ranging over a primitive set A is universally bounded over all choices for A. In 1988 he asked if this universal bound is attained by the set of prime numbers. One source of difficulty in this conjecture is that ∑n−λ over a primitive set is maximized by the primes if and only if λ is at least the critical exponent τ1 ≈ 1.14. A set is k-primitive if no member divides any product of up to k other distinct members. One may similarly consider the critical exponent τk for which the primes are maximal among k-primitive sets. In recent work the authors showed that τ2 < 0.8, which directly implies the Erdős conjecture for 2-primitive sets. In this article we study the limiting behavior of the critical exponent, proving that τk tends to zero as k → ∞.
      PubDate: 2022-10-01
       
 
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