奇特的向日葵

IF 0.9 2区 数学 Q2 MATHEMATICS
Peter Frankl , János Pach , Dömötör Pálvölgyi
{"title":"奇特的向日葵","authors":"Peter Frankl ,&nbsp;János Pach ,&nbsp;Dömötör Pálvölgyi","doi":"10.1016/j.jcta.2024.105889","DOIUrl":null,"url":null,"abstract":"<div><p>Extending the notion of sunflowers, we call a family of at least two sets an <em>odd-sunflower</em> if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <span><math><mi>μ</mi><mo>&lt;</mo><mn>2</mn></math></span> such that every family of subsets of an <em>n</em>-element set that contains no odd-sunflower consists of at most <span><math><msup><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> sets. We construct such families of size at least <span><math><msup><mrow><mn>1.5021</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We also characterize minimal odd-sunflowers of triples.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"206 ","pages":"Article 105889"},"PeriodicalIF":0.9000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0097316524000281/pdfft?md5=4524ddd068e6ba4b9569281736257e67&pid=1-s2.0-S0097316524000281-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Odd-sunflowers\",\"authors\":\"Peter Frankl ,&nbsp;János Pach ,&nbsp;Dömötör Pálvölgyi\",\"doi\":\"10.1016/j.jcta.2024.105889\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Extending the notion of sunflowers, we call a family of at least two sets an <em>odd-sunflower</em> if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <span><math><mi>μ</mi><mo>&lt;</mo><mn>2</mn></math></span> such that every family of subsets of an <em>n</em>-element set that contains no odd-sunflower consists of at most <span><math><msup><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> sets. We construct such families of size at least <span><math><msup><mrow><mn>1.5021</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We also characterize minimal odd-sunflowers of triples.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":\"206 \",\"pages\":\"Article 105889\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0097316524000281/pdfft?md5=4524ddd068e6ba4b9569281736257e67&pid=1-s2.0-S0097316524000281-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316524000281\",\"RegionNum\":2,\"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":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524000281","RegionNum":2,"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

扩展向日葵的概念,如果底层集合的每个元素都包含在奇数个集合中或不包含在任何一个集合中,我们就称至少有两个集合的族为奇数向日葵。根据最近由纳斯伦德和萨温证明的厄尔多斯-塞梅雷迪猜想,存在一个常数 μ<2,使得不包含奇数向日葵的 n 元素集合的每个子集族至多由 μn 个集合组成。我们构建的这种族的大小至少为 1.5021n。我们还描述了三元组的最小奇数太阳花的特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Odd-sunflowers

Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant μ<2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most μn sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples.

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
CiteScore
2.90
自引率
9.10%
发文量
94
审稿时长
12 months
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信