Statistics for S acting on k-sets

Nick Gill; Bianca Lodà

doi:10.1016/j.jalgebra.2021.10.037

Statistics for S acting on k-sets

Nick Gill, Bianca Lodà

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Abstract

We study the natural action of Sn 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, 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.

Original language	English
Article number	S0021869321005366
Journal	Journal of Algebra
Volume	00
Issue number	00
Early online date	15 Nov 2021
DOIs	https://doi.org/10.1016/j.jalgebra.2021.10.037
Publication status	E-pub ahead of print - 15 Nov 2021

Keywords

permutation group
height of a permutation group
relational complexity
base size

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10.1016/j.jalgebra.2021.10.037

Accepted ManuscriptAccepted author manuscript, 182 KBLicence: CC BY-NC-ND

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title = "Statistics for S acting on k-sets",

abstract = "We study the natural action of Sn 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, 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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AU - Lodà, Bianca

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N2 - We study the natural action of Sn 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, 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.

AB - We study the natural action of Sn 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, 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.

KW - permutation group

KW - height of a permutation group

KW - relational complexity

KW - base size

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DO - 10.1016/j.jalgebra.2021.10.037

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JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 00

M1 - S0021869321005366

ER -

Statistics for S acting on k-sets

Abstract

Keywords

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