Statistics for Sn acting on k-sets

Gill, N. and Lodà, B. (2021). Statistics for Sn acting on k-sets. Journal of Algebra (Early access).

DOI: https://doi.org/10.1016/j.jalgebra.2021.10.037

Abstract

We study the natural action of Sn on the set of k-subsets of the set {1,…,n} when [Formula presented]. 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, the 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.

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