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A Generalisation of Sperner's Theorem Using Weighted Chains

2025/09/30 by Dillies, Yaël, Johnson, Matthew, Kowalska, Aleksandra
#05D05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.26493

Abstract

We find the (unique) largest subset of \0, 1, 2\n such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most k coordinates. To do so, we decompose the cube into weighted chains. In Appendix B we present a new proof of Sperner's theorem we found while working on this problem.

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