Journal of Combinatorial Theory Series A最新文献_第6页

On non-empty cross-t-intersecting families 关于非空交叉相交族

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-24 DOI: 10.1016/j.jcta.2024.105960

Anshui Li , Huajun Zhang

引用次数: 0

Avoiding intersections of given size in finite affine spaces AG(n,2) 在有限仿射空间 AG(n,2) 中避免给定大小的交集

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-24 DOI: 10.1016/j.jcta.2024.105959

Benedek Kovács , Zoltán Lóránt Nagy

{"title":"Avoiding intersections of given size in finite affine spaces AG(n,2)","authors":"Benedek Kovács , Zoltán Lóránt Nagy","doi":"10.1016/j.jcta.2024.105959","DOIUrl":"10.1016/j.jcta.2024.105959","url":null,"abstract":"<div><div>We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size <math><mi>m</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>]</mo></math> of the n-dimensional binary affine space <math><mrow><mi>AG</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mn>2</mn><mo>)</mo></math>. Following the theme of Erdős, Füredi, Rothschild and T. Sós, we partially determine which local densities in k-dimensional affine subspaces are unavoidable in all m-element point sets in the n-dimensional affine space.</div><div>We also show constructions of point sets for which the intersection sizes with k-dimensional affine subspaces take values from a set of a small size compared to <math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></math>. These are built up from affine subspaces and so-called subspace evasive sets. Meanwhile, we improve the best known upper bounds on subspace evasive sets and apply results concerning the canonical signed-digit (CSD) representation of numbers.</div><div>Keywords: unavoidable, affine subspaces, evasive sets, random methods, canonical signed-digit number system.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"209 ","pages":"Article 105959"},"PeriodicalIF":0.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0097316524000980/pdfft?md5=62687b67d599290d3f204041642a9a6a&pid=1-s2.0-S0097316524000980-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A rank two Leonard pair in Terwilliger algebras of Doob graphs Doob 图的特威里格代数中的二阶伦纳德对

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-23 DOI: 10.1016/j.jcta.2024.105958

John Vincent S. Morales

{"title":"A rank two Leonard pair in Terwilliger algebras of Doob graphs","authors":"John Vincent S. Morales","doi":"10.1016/j.jcta.2024.105958","DOIUrl":"10.1016/j.jcta.2024.105958","url":null,"abstract":"<div><div>Let <math><mi>Γ</mi><mo>=</mo><mi>Γ</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></math> denote the Doob graph formed by the Cartesian product of the nth Cartesian power of the Shrikhande graph and the mth Cartesian power of the complete graph on four vertices. Let <math><mi>T</mi><mo>=</mo><mi>T</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> denote the Terwilliger algebra of Γ with respect to a fixed vertex x of Γ and let W denote an arbitrary non-thin irreducible T-module in the standard module of Γ. In (Morales and Palma, 2021 [25]), it was shown that there exists a Lie algebra embedding π from the special orthogonal algebra <math><msub><mrow><mi>so</mi></mrow><mrow><mn>4</mn></mrow></msub></math> into T and that W is an irreducible <math><mi>π</mi><mo>(</mo><msub><mrow><mi>so</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>)</mo></math>-module. In this paper, we consider two Cartan subalgebras <math><mi>h</mi><mo>,</mo><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> of <math><msub><mrow><mi>so</mi></mrow><mrow><mn>4</mn></mrow></msub></math> such that <math><mi>h</mi><mo>,</mo><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> generate <math><msub><mrow><mi>so</mi></mrow><mrow><mn>4</mn></mrow></msub></math>. Using the embedding <math><mi>π</mi><mo>:</mo><msub><mrow><mi>so</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>→</mo><mi>T</mi></math>, we show that <math><mi>π</mi><mo>(</mo><mi>h</mi><mo>)</mo></math> and <math><mi>π</mi><mo>(</mo><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math> act on W as a rank two Leonard pair. We also obtain several direct sum decompositions of W akin to how split decompositions are obtained from Leonard pairs of rank one.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"210 ","pages":"Article 105958"},"PeriodicalIF":0.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Covering the set of p-elements in finite groups by proper subgroups 用适当的子群覆盖有限群中 p 元素的集合

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-20 DOI: 10.1016/j.jcta.2024.105954

Attila Maróti , Juan Martínez , Alexander Moretó

引用次数: 0

Proofs of some conjectures of Merca on truncated series involving the Rogers-Ramanujan functions 梅尔卡关于涉及罗杰斯-拉马努扬函数的截断数列的一些猜想的证明

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-19 DOI: 10.1016/j.jcta.2024.105956

Yongqiang Chen, Olivia X.M. Yao

引用次数: 0

On the proportion of metric matroids whose Jacobians have nontrivial p-torsion 关于雅各布有非三角 p 扭转的公因子矩阵的比例

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-16 DOI: 10.1016/j.jcta.2024.105953

Sergio Ricardo Zapata Ceballos

引用次数: 0

Approximate generalized Steiner systems and near-optimal constant weight codes 近似广义斯泰纳系统和近优恒定权重码

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-11 DOI: 10.1016/j.jcta.2024.105955

Miao Liu , Chong Shangguan

{"title":"Approximate generalized Steiner systems and near-optimal constant weight codes","authors":"Miao Liu , Chong Shangguan","doi":"10.1016/j.jcta.2024.105955","DOIUrl":"10.1016/j.jcta.2024.105955","url":null,"abstract":"<div>Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for all fixed odd distances, there exist near-optimal CWCs and CCCs asymptotically achieving the classic Johnson-type upper bounds.Let <math><msub><mrow><mi>A</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>w</mi><mo>)</mo></math> denote the maximum size of q-ary CWCs of length n with constant weight w and minimum distance d. One of our main results shows that for all fixed <math><mi>q</mi><mo>,</mo><mi>w</mi></math> and odd d, one has <math><msub><mrow><mi>lim</mi></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></msub><mo>⁡</mo><mfrac><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow><mrow><mo>(</mo><mtable><mtr><mtd><mi>n</mi></mtd></mtr><mtr><mtd><mi>t</mi></mtd></mtr></mtable><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>t</mi></mrow></msup></mrow><mrow><mo>(</mo><mtable><mtr><mtd><mi>w</mi></mtd></mtr><mtr><mtd><mi>t</mi></mtd></mtr></mtable><mo>)</mo></mrow></mfrac></math>, where <math><mi>t</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>w</mi><mo>−</mo><mi>d</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>. This implies the existence of near-optimal generalized Steiner systems originally introduced by Etzion, and can be viewed as a counterpart of a celebrated result of Rödl on the existence of near-optimal Steiner systems. Note that prior to our work, very little is known about <math><msub><mrow><mi>A</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>w</mi><mo>)</mo></math> for <math><mi>q</mi><mo>≥</mo><mn>3</mn></math>. A similar result is proved for the maximum size of CCCs.We provide different proofs for our two main results, based on two strengthenings of the well-known Frankl-Rödl-Pippenger theorem on the existence of near-optimal matchings in hypergraphs: the first proof follows by Kahn's linear programming variation of the above theorem, and the second follows by the recent independent work of Delcourt-Postle, and Glock-Joos-Kim-Kühn-Lichev on the existence of near-optimal matchings avoiding certain forbidden configurations.We also present several intriguing open questions for future research.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"209 ","pages":"Article 105955"},"PeriodicalIF":0.9,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0097316524000943/pdfft?md5=65eb96db9a426be78f5105ffe48c2ece&pid=1-s2.0-S0097316524000943-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A note on tournament m-semiregular representations of finite groups 关于有限群 m-semiregular 代表锦标赛的说明

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-09-04 DOI: 10.1016/j.jcta.2024.105952

Jia-Li Du

{"title":"A note on tournament m-semiregular representations of finite groups","authors":"Jia-Li Du","doi":"10.1016/j.jcta.2024.105952","DOIUrl":"10.1016/j.jcta.2024.105952","url":null,"abstract":"<div>For a positive integer m, a group G is said to admit a tournament m-semiregular representation (TmSR for short) if there exists a tournament Γ such that the automorphism group of Γ is isomorphic to G and acts semiregularly on the vertex set of Γ with m orbits. It is easy to see that every finite group of even order does not admit a TmSR for any positive integer m. The T1SR is the well-known tournament regular representation (TRR for short). In 1970s, Babai and Imrich proved that every finite group of odd order admits a TRR except for <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math>, and every group (finite or infinite) without element of order 2 having an independent generating set admits a T2SR in (1979) [3]. Later, Godsil correct the result by showing that the only finite groups of odd order without a TRR are <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math> and <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></msubsup></math> by a probabilistic approach in (1986) [11]. In this note, it is shown that every finite group of odd order has a TmSR for every <math><mi>m</mi><mo>≥</mo><mn>2</mn></math>.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"209 ","pages":"Article 105952"},"PeriodicalIF":0.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0097316524000918/pdfft?md5=9f9703a561ce567e377942546fcc91e2&pid=1-s2.0-S0097316524000918-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The separating Noether number of abelian groups of rank two 二阶无性群的分离诺特数

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-08-29 DOI: 10.1016/j.jcta.2024.105951

Barna Schefler

引用次数: 0

Young tableau reconstruction via minors 通过未成年人重建幼年台构图

IF 0.9 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-08-26 DOI: 10.1016/j.jcta.2024.105950

William Q. Erickson, Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski, Cordell Hammon, Jasmin Mohn, Indalecio Ruiz-Bolanos

{"title":"Young tableau reconstruction via minors","authors":"William Q. Erickson, Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski, Cordell Hammon, Jasmin Mohn, Indalecio Ruiz-Bolanos","doi":"10.1016/j.jcta.2024.105950","DOIUrl":"10.1016/j.jcta.2024.105950","url":null,"abstract":"<div>The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau T, a 1-minor of T is a tableau obtained by first deleting any cell of T, and then performing jeu de taquin slides to fill the resulting gap. This can be iterated to arrive at the set of k-minors of T. The problem is this: given k, what are the values of n such that every tableau of size n can be reconstructed from its set of k-minors? For <math><mi>k</mi><mo>=</mo><mn>1</mn></math>, the problem was recently solved by Cain and Lehtonen. In this paper, we solve the problem for <math><mi>k</mi><mo>=</mo><mn>2</mn></math>, proving the sharp lower bound <math><mi>n</mi><mo>≥</mo><mn>8</mn></math>. In the case of multisets of k-minors, we also give a lower bound for arbitrary k, as a first step toward a sharp bound in the general multiset case.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"209 ","pages":"Article 105950"},"PeriodicalIF":0.9,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S009731652400089X/pdfft?md5=9b63472f7cd5508023664fdfaa81b914&pid=1-s2.0-S009731652400089X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0