非平凡的r明智的同意家庭

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-02-11 DOI:10.1016/j.ejc.2025.104129

Peter Frankl , Andrey Kupavskii

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引用次数: 0

摘要

[n]的子集族是r明智的，如果对于族中的任何r个集合存在一个元素x，该元素x要么包含在所有r个集合中，要么不包含在任何r个集合中。这类族的研究是由离散优化问题驱动的。在本文中，我们确定了最大的非平凡r-wise同意族的大小。这可以看作是经典布雷斯-戴金定理的推广。

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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Non-trivial r-wise agreeing families

A family of subsets of

[n]

r

-wise agreeing if for any

r

sets from the family there is an element

x

that is either contained in all or contained in none of the

r

sets. The study of such families is motivated by questions in discrete optimization. In this paper, we determine the size of the largest non-trivial

r

-wise agreeing family. This can be seen as a generalization of the classical Brace–Daykin theorem.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.