Families that remain k-Sperner even after omitting an element of their ground set

2012/07/12 by Patkos, Balazs
#05D05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.2923

Abstract

A family \cF⊆ 2^[n] of sets is said to be l-trace k-Sperner if for any l-subset L ⊂ [n] the family \cF|_L=\F|_L:F ∈ \cF\=\F ∩ L: F ∈ \cF\ is k-Sperner, i.e. does not contain any chain of length k+1. The maximum size that an l-trace k-Sperner family \cF ⊆ 2^[n] can have is denoted by f(n,k,l). For pairs of integers l

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