集合具有不同集合的系统

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.004

Javier Cilleruelo , Oriol Serra , Maximilian Wötzel

引用次数: 0

摘要

如果集合A+A '，A,A '∈A是两两不同的，则由{1,2，…，N}的k个子集组成的族A是一个西顿系统。证明了由[N]的k个子集组成的Sidon系统的最大基数Fk(N)满足Fk(N)≤(N−1k−1)+N−k，且其渐近下界Fk(N)=Ωk(Nk−1)。当k≤3时，得到了Fk(N)上更精确的界。我们还得到了k=2和3时随机系统为Sidon的阈值概率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Set systems with distinct sumsets

A family $A$ of k-subsets of ${1, 2, \dots, N}$ is a Sidon system if the sumsets $A + A^{'}, A, A^{'} \in A$ are pairwise distinct. We show that the largest cardinality $F_{k} (N)$ of a Sidon system of k-subsets of $[N]$ satisfies $F_{k} (N) \leq (\begin{matrix} N - 1 \\ k - 1 \end{matrix}) + N - k$ and the asymptotic lower bound $F_{k} (N) = Ω_{k} (N^{k - 1})$ . More precise bounds on $F_{k} (N)$ are obtained for $k \leq 3$ . We also obtain the threshold probability for a random system to be Sidon for $k = 2$ and 3.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.