中文版 | English
Title

On the maximum size of 3-uniform U(s, q) families

Alternative Title
关于 3 元一致 U(s, q) 集族的最大基数
Author
Corresponding AuthorXiang,Qing
Publication Years
2023
DOI
Source Title
ISSN
1674-7216
EISSN
2095-9427
Volume53Issue:2Pages:369-380
Abstract

Let n, k, s, q be integers, n > q > k, sk > q and s > 2. A family F ⊂ is U(s, q) if |F1∪···∪Fs| 6 q for any F1, . . ., Fs ∈ F. This notion was introduced recently by Frankl and Kupavskii (2021) and it generalizes the property of a family being t-intersecting, or having no more than s pairwise disjoint members. Frankl and Kupavskii (2021) formulated a problem of finding the maximum size of U(s, q) families. In this paper, we study the k = 3 case extensively, and determine the maximum size of U(s, 2s+t) families for all s > s0(t) and all meaningful n and q. In particular, we prove a conjecture proposed by Frankl and Kupavskii (2021) on the maximum size of 3-uniform U(s, q) families.

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URL[Source Record]
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Language
Chinese
SUSTech Authorship
First ; Corresponding
Citation statistics
Cited Times [WOS]:0
Document TypeJournal Article
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/527597
DepartmentDepartment of Mathematics
Affiliation
1.南方科技大学数学系, 深圳 518055
2.南科大杰曼诺夫数学中心, 深圳 518055
3.浙江大学数学科学学院, 杭州 310027
First Author AffilicationDepartment of Mathematics
Corresponding Author AffilicationDepartment of Mathematics
First Author's First AffilicationDepartment of Mathematics
Recommended Citation
GB/T 7714
Xiang,Qing,Zou,Hanlin. On the maximum size of 3-uniform U(s, q) families[J]. Scientia Sinica Mathematica,2023,53(2):369-380.
APA
Xiang,Qing,&Zou,Hanlin.(2023).On the maximum size of 3-uniform U(s, q) families.Scientia Sinica Mathematica,53(2),369-380.
MLA
Xiang,Qing,et al."On the maximum size of 3-uniform U(s, q) families".Scientia Sinica Mathematica 53.2(2023):369-380.
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关于3元一致.pdf(288KB) Restricted Access--
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