Statistics for S_n acting on k-sets

Gill, N. and Lodà, B. (2022). Statistics for S_n acting on k-sets. Journal of Algebra, 607(Part A) pp. 286–299.

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 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, 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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI