Statistics for S_n acting on k-sets

2021/01/21 by Gill, Nick, Lodá, Bianca
#20B30 (Primary) 20B05 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2101.08644

Abstract

We study the natural action of S_n on the set of k-subsets of the set \1,…, n\ when 1≤ k ≤ (n)/(2). For this action we calculate the maximum size of a minimal base, the height and the maximum length of an irredundant base. Here a "base" is a set with trivial pointwise stabilizer, "height" is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an "irredundant base" can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.

Related

• Set Systems with Covering Properties and Low VC-Dimension
• Set partition patterns and statistics
• Improved stability for the size and structure of sumsets
• Set Systems and Families of Permutations with Small Traces
• Set families with a forbidden induced subposet