Pub Date : 2024-12-09DOI: 10.1016/j.disc.2024.114352
Ian Gossett
We define Z-signable correspondence assignments on multigraphs, which generalize good correspondence assignments as introduced by Kaul and Mudrock. We introduce an auxiliary digraph that allows us to prove an Alon-Tarsi style theorem for DP-colorings from Z-signable correspondence assignments on multigraphs, and apply this theorem to obtain three DP-coloring analogs of the Alon-Tarsi theorem for arbitrary correspondence assignments as corollaries. We illustrate the use of these corollaries for DP-colorings on a restricted class of correspondence assignments on toroidal grids.
{"title":"Some orientation theorems for restricted DP-colorings of graphs","authors":"Ian Gossett","doi":"10.1016/j.disc.2024.114352","DOIUrl":"10.1016/j.disc.2024.114352","url":null,"abstract":"<div><div>We define <em>Z-signable</em> correspondence assignments on multigraphs, which generalize <em>good</em> correspondence assignments as introduced by Kaul and Mudrock. We introduce an auxiliary digraph that allows us to prove an Alon-Tarsi style theorem for DP-colorings from <em>Z</em>-signable correspondence assignments on multigraphs, and apply this theorem to obtain three DP-coloring analogs of the Alon-Tarsi theorem for arbitrary correspondence assignments as corollaries. We illustrate the use of these corollaries for DP-colorings on a restricted class of correspondence assignments on toroidal grids.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114352"},"PeriodicalIF":0.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143171263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-05DOI: 10.1016/j.disc.2024.114348
Pallabi Manna , Santanu Mandal , Andrea Lucchini
Let G be a finite group and let be the undirected power graph of G. Recall that the vertices of are labelled by the elements of G, with an edge between and if either or . The subgraph induced by the non-identity elements is called the reduced power graph, denoted by . The main purpose of this paper is to investigate the finite groups whose reduced power graph is claw-free, which means that it has no vertex with three pairwise non-adjacent neighbours. In particular, we prove that if is claw-free, then either G is solvable or G is an almost simple group. In the second case, the socle of G is isomorphic to for suitable choices of q. Finally we prove that if is claw-free, then the order of G is divisible by at most 5 different primes.
{"title":"On finite groups whose power graph is claw-free","authors":"Pallabi Manna , Santanu Mandal , Andrea Lucchini","doi":"10.1016/j.disc.2024.114348","DOIUrl":"10.1016/j.disc.2024.114348","url":null,"abstract":"<div><div>Let <em>G</em> be a finite group and let <span><math><mi>P</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the undirected power graph of <em>G</em>. Recall that the vertices of <span><math><mi>P</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> are labelled by the elements of <em>G</em>, with an edge between <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> if either <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mo>〈</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>〉</mo></math></span> or <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mo>〈</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>〉</mo></math></span>. The subgraph induced by the non-identity elements is called the reduced power graph, denoted by <span><math><msup><mrow><mi>P</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The main purpose of this paper is to investigate the finite groups whose reduced power graph is claw-free, which means that it has no vertex with three pairwise non-adjacent neighbours. In particular, we prove that if <span><math><msup><mrow><mi>P</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is claw-free, then either <em>G</em> is solvable or <em>G</em> is an almost simple group. In the second case, the socle of <em>G</em> is isomorphic to <span><math><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></math></span> for suitable choices of <em>q</em>. Finally we prove that if <span><math><msup><mrow><mi>P</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is claw-free, then the order of <em>G</em> is divisible by at most 5 different primes.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114348"},"PeriodicalIF":0.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-04DOI: 10.1016/j.disc.2024.114346
Sarah Allred , Guoli Ding , Bogdan Oporowski
In 1930, Ramsey proved that every infinite graph contains either an infinite clique or an infinite independent set. König proved that every connected infinite graph contains either a ray or a vertex of infinite degree. In this paper, we establish the 2-connected analog of these results.
{"title":"Unavoidable induced subgraphs of infinite 2-connected graphs","authors":"Sarah Allred , Guoli Ding , Bogdan Oporowski","doi":"10.1016/j.disc.2024.114346","DOIUrl":"10.1016/j.disc.2024.114346","url":null,"abstract":"<div><div>In 1930, Ramsey proved that every infinite graph contains either an infinite clique or an infinite independent set. König proved that every connected infinite graph contains either a ray or a vertex of infinite degree. In this paper, we establish the 2-connected analog of these results.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114346"},"PeriodicalIF":0.7,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143171267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-02DOI: 10.1016/j.disc.2024.114347
Petr Hliněný, Michal Korbela
A recent result of Bokal et al. (2022) [3] proved that the exact minimum value of c such that c-crossing-critical graphs do not have bounded maximum degree is . The key to that result is an inductive construction of a family of 13-crossing-critical graphs with many vertices of arbitrarily high degrees. While the inductive part of the construction is rather easy, it all relies on the fact that a certain 17-vertex base graph has the crossing number 13, which was originally verified only by a machine-readable computer proof. We provide a relatively short self-contained computer-free proof of the latter fact. Furthermore, we subsequently generalize the critical construction in order to provide a definitive answer to another long-standing question of this research area; we prove that for every and integers , there exists a c-crossing-critical graph with more than q vertices of each of the degrees .
{"title":"On 13-crossing-critical graphs with arbitrarily large degrees","authors":"Petr Hliněný, Michal Korbela","doi":"10.1016/j.disc.2024.114347","DOIUrl":"10.1016/j.disc.2024.114347","url":null,"abstract":"<div><div>A recent result of Bokal et al. (2022) <span><span>[3]</span></span> proved that the exact minimum value of <em>c</em> such that <em>c</em>-crossing-critical graphs do <em>not</em> have bounded maximum degree is <span><math><mi>c</mi><mo>=</mo><mn>13</mn></math></span>. The key to that result is an inductive construction of a family of 13-crossing-critical graphs with many vertices of arbitrarily high degrees. While the inductive part of the construction is rather easy, it all relies on the fact that a certain 17-vertex base graph has the crossing number 13, which was originally verified only by a machine-readable computer proof. We provide a relatively short self-contained computer-free proof of the latter fact. Furthermore, we subsequently generalize the critical construction in order to provide a definitive answer to another long-standing question of this research area; we prove that for every <span><math><mi>c</mi><mo>≥</mo><mn>13</mn></math></span> and integers <span><math><mi>d</mi><mo>,</mo><mi>q</mi></math></span>, there exists a <em>c</em>-crossing-critical graph with more than <em>q</em> vertices of <em>each</em> of the degrees <span><math><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114347"},"PeriodicalIF":0.7,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-29DOI: 10.1016/j.disc.2024.114345
Sho Kubota , Hiroto Sekido , Kiyoto Yoshino
The interest of this paper is a characterization of graphs that induce periodic Grover walks with given periods. In previous studies, Yoshie has shown that the only graphs that induce odd periodic Grover walks are cycle graphs. However, this problem is largely unsolved for even periods. In this study, we show that regular graphs that induce 2l-periodic Grover walks are also cycle graphs in most cases, where l is an odd integer. The proof uses Galois theory.
{"title":"Regular graphs to induce even periodic Grover walks","authors":"Sho Kubota , Hiroto Sekido , Kiyoto Yoshino","doi":"10.1016/j.disc.2024.114345","DOIUrl":"10.1016/j.disc.2024.114345","url":null,"abstract":"<div><div>The interest of this paper is a characterization of graphs that induce periodic Grover walks with given periods. In previous studies, Yoshie has shown that the only graphs that induce odd periodic Grover walks are cycle graphs. However, this problem is largely unsolved for even periods. In this study, we show that regular graphs that induce 2<em>l</em>-periodic Grover walks are also cycle graphs in most cases, where <em>l</em> is an odd integer. The proof uses Galois theory.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114345"},"PeriodicalIF":0.7,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1016/j.disc.2024.114332
Pierre-Antoine Bernard , Nicolas Crampé , Luc Vinet , Meri Zaimi , Xiaohong Zhang
The bivariate P- and Q-polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomials which form the eigenvalues of the scheme. These bispectral properties are obtained from contiguity relations of univariate dual q-Hahn and affine q-Krawtchouk polynomials. The bispectral algebra associated to the bivariate polynomials is investigated, as well as the subconstituent algebra of the schemes. The properties of the schemes are compared to those of the non-binary Johnson schemes through a limit.
{"title":"Bivariate P- and Q-polynomial structures of the association schemes based on attenuated spaces","authors":"Pierre-Antoine Bernard , Nicolas Crampé , Luc Vinet , Meri Zaimi , Xiaohong Zhang","doi":"10.1016/j.disc.2024.114332","DOIUrl":"10.1016/j.disc.2024.114332","url":null,"abstract":"<div><div>The bivariate <em>P</em>- and <em>Q</em>-polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomials which form the eigenvalues of the scheme. These bispectral properties are obtained from contiguity relations of univariate dual <em>q</em>-Hahn and affine <em>q</em>-Krawtchouk polynomials. The bispectral algebra associated to the bivariate polynomials is investigated, as well as the subconstituent algebra of the schemes. The properties of the schemes are compared to those of the non-binary Johnson schemes through a limit.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114332"},"PeriodicalIF":0.7,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-27DOI: 10.1016/j.disc.2024.114336
Rebecca Bourn , William Q. Erickson
We prove a conjecture of Bourn and Willenbring (2020) regarding the palindromicity and unimodality of a certain family of polynomials . These recursively defined polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD). The key to our proof is showing that the defining recursion can be viewed as describing sums of symmetric differences of pairs of Young diagrams; in this setting, palindromicity is equivalent to the preservation of the symmetric difference under the transposition of diagrams. We also observe a connection to recent work by Defant et al. (2024) on the Wiener index of minuscule lattices, which we reinterpret combinatorially to obtain explicit formulas for the coefficients of and for the expected value of the discrete EMD.
{"title":"Palindromicity of the numerator of a statistical generating function","authors":"Rebecca Bourn , William Q. Erickson","doi":"10.1016/j.disc.2024.114336","DOIUrl":"10.1016/j.disc.2024.114336","url":null,"abstract":"<div><div>We prove a conjecture of Bourn and Willenbring (2020) regarding the palindromicity and unimodality of a certain family of polynomials <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. These recursively defined polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD). The key to our proof is showing that the defining recursion can be viewed as describing sums of symmetric differences of pairs of Young diagrams; in this setting, palindromicity is equivalent to the preservation of the symmetric difference under the transposition of diagrams. We also observe a connection to recent work by Defant et al. (2024) on the Wiener index of minuscule lattices, which we reinterpret combinatorially to obtain explicit formulas for the coefficients of <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and for the expected value of the discrete EMD.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114336"},"PeriodicalIF":0.7,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-27DOI: 10.1016/j.disc.2024.114335
Mohammad Farrokhi D.G. , Alireza Shamsian , Ali Akbar Yazdan Pour
Given an arbitrary hypergraph , we may glue to a family of hypergraphs to get a new hypergraph having as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph is under control in terms of the glued components. This enables us to construct broad classes of simplicial complexes containing a given simplicial complex as induced subcomplex satisfying nice topological and combinatorial properties. Our results will be accompanied with some interesting open problems.
给定一个任意的超图 H，我们可以将一个超图族粘合到 H 上，从而得到一个以 H 为诱导子超图的新超图 H′。在本文中，我们介绍了三种粘合技术，其拓扑和组合特性（如科恩-马科拉伊性、可脱壳性、顶点可分解性等）都可以通过粘合成分来控制。这使我们能够构造出一大类简单复数，其中包含一个给定简单复数作为诱导子复数，并满足良好的拓扑和组合特性。我们的成果将伴随着一些有趣的开放性问题。
{"title":"Extending simplicial complexes: Topological and combinatorial properties","authors":"Mohammad Farrokhi D.G. , Alireza Shamsian , Ali Akbar Yazdan Pour","doi":"10.1016/j.disc.2024.114335","DOIUrl":"10.1016/j.disc.2024.114335","url":null,"abstract":"<div><div>Given an arbitrary hypergraph <span><math><mi>H</mi></math></span>, we may glue to <span><math><mi>H</mi></math></span> a family of hypergraphs to get a new hypergraph <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> having <span><math><mi>H</mi></math></span> as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> is under control in terms of the glued components. This enables us to construct broad classes of simplicial complexes containing a given simplicial complex as induced subcomplex satisfying nice topological and combinatorial properties. Our results will be accompanied with some interesting open problems.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114335"},"PeriodicalIF":0.7,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.disc.2024.114333
Diane Donovan, Tara Kemp, James Lefevre
For an integer partition , a 2-realization of this partition is a latin square of order N with disjoint subsquares of orders . The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to m-ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original.
对于 h1+...+hn=N 的整数分割，该分割的 2 重化是一个 N 阶拉丁方阵，其子方阵的阶数为 h1，...，hn。2 重化的存在是富克斯提出的一个已部分解决的问题。在本文中，我们将福克斯的问题扩展到 mary 准群，或者等价于拉丁超立方。我们为最多有两个不同部分的一些分区构造了拉丁立方体，并强调了新问题与原问题的关系。
{"title":"Latin hypercubes realizing integer partitions","authors":"Diane Donovan, Tara Kemp, James Lefevre","doi":"10.1016/j.disc.2024.114333","DOIUrl":"10.1016/j.disc.2024.114333","url":null,"abstract":"<div><div>For an integer partition <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>…</mo><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>N</mi></math></span>, a 2-realization of this partition is a latin square of order <em>N</em> with disjoint subsquares of orders <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. The existence of 2-realizations is a partially solved problem posed by Fuchs. In this paper, we extend Fuchs' problem to <em>m</em>-ary quasigroups, or, equivalently, latin hypercubes. We construct latin cubes for some partitions with at most two distinct parts and highlight how the new problem is related to the original.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114333"},"PeriodicalIF":0.7,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.disc.2024.114334
Jakob Führer , Jozsef Solymosi
Let be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, wicket, is formed by three rows and two columns of a point matrix. In this note, we give a new lower bound on the Turán number of wickets using estimates on cap sets. We also show that this problem is closely connected to important questions in additive combinatorics.
{"title":"Caps and wickets","authors":"Jakob Führer , Jozsef Solymosi","doi":"10.1016/j.disc.2024.114334","DOIUrl":"10.1016/j.disc.2024.114334","url":null,"abstract":"<div><div>Let <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></msubsup></math></span> be a 3-uniform linear hypergraph, i.e. any two edges have at most one vertex common. A special hypergraph, <em>wicket</em>, is formed by three rows and two columns of a <span><math><mn>3</mn><mo>×</mo><mn>3</mn></math></span> point matrix. In this note, we give a new lower bound on the Turán number of wickets using estimates on cap sets. We also show that this problem is closely connected to important questions in additive combinatorics.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 3","pages":"Article 114334"},"PeriodicalIF":0.7,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号