Large sum-free sets in Z5n

IF 0.9 2区 数学 Q2 MATHEMATICS Journal of Combinatorial Theory Series A Pub Date : 2024-02-02 DOI:10.1016/j.jcta.2024.105865
Vsevolod F. Lev
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Abstract

It is well-known that for a prime p2(mod3) and integer n1, the maximum possible size of a sum-free subset of the elementary abelian group Zpn is 13(p+1)pn1. However, the matching stability result is known for p=2 only. We consider the first open case p=5 showing that if AZ5n is a sum-free subset with |A|>325n1, then there are a subgroup H<Z5n of size |H|=5n1 and an element eH such that A(e+H)(e+H).

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Z5n 中的大无和集
众所周知,对于素数 p≡2(mod3)和整数 n≥1,初等无方组 Zpn 的无和子集的最大可能大小为 13(p+1)pn-1。然而,已知的匹配稳定性结果仅适用于 p=2。我们考虑第一种开放情况 p=5 表明,如果 A⊆Z5n 是|A|>32⋅5n-1 的无和子集,那么存在大小为 |H|=5n-1的子群 H<Z5n 和元素 e∉H,使得 A⊆(e+H)∪(-e+H)。
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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.
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