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.

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About

• Item ORO ID
• 81573
• Item Type
• Journal Item
• ISSN
• 0021-8693
• Keywords
• permutation group; height of a permutation group; relational complexity; base size
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2021 Published by Elsevier Inc.
• Related URLs
• • https://pure.southwales.ac.uk/en/publica...(Other)
• Depositing User
• Nick Gill