On L-close Sperner systems

2019/08/05 by Nagy, Daniel, Patkos, Balazs
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.01744

Abstract

For a set L of positive integers, a set system F ⊆ 2^[n] is said to be L-close Sperner, if for any pair F,G of distinct sets in F the skew distance sd(F,G)=min\|F∖ G|,|G∖ F|\ belongs to L. We reprove an extremal result of Boros, Gurvich, and Milani\v c on the maximum size of L-close Sperner set systems for L=\1\ and generalize to |L|=1 and obtain slightly weaker bounds for arbitrary L. We also consider the problem when L might include 0 and reprove a theorem of Frankl, Füredi, and Pach on the size of largest set systems with all skew distances belonging to L=\0,1\.

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