帽子和小门

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-26 DOI:10.1016/j.disc.2024.114334

Jakob Führer , Jozsef Solymosi

{"title":"帽子和小门","authors":"Jakob Führer , Jozsef Solymosi","doi":"10.1016/j.disc.2024.114334","DOIUrl":null,"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":0.7000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Caps and wickets\",\"authors\":\"Jakob Führer , Jozsef Solymosi\",\"doi\":\"10.1016/j.disc.2024.114334\",\"DOIUrl\":null,\"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\":0.7000,\"publicationDate\":\"2024-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24004655\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004655","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

假设 Hn(3) 是一个 3-uniform 线性超图，即任意两条边最多有一个共同顶点。一种特殊的超图，即 wicket，由 3×3 点矩阵的三行两列构成。在本论文中，我们利用对上限集的估计，给出了图兰数 wicket 的新下限。我们还证明了这一问题与加法组合学中的重要问题密切相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Caps and wickets

Let

H_{n}^{(3)}

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

3 \times 3

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.