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

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

2 Wedi eu Llwytho i Lawr (Pure)

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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.

Iaith wreiddiol	Saesneg
Rhif yr erthygl	S0021869321005366
Cyfnodolyn	Journal of Algebra
Cyfrol	00
Rhif cyhoeddi	00
Dyddiad ar-lein cynnar	15 Tach 2021
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1016/j.jalgebra.2021.10.037
Statws	E-gyhoeddi cyn argraffu - 15 Tach 2021

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10.1016/j.jalgebra.2021.10.037

Accepted ManuscriptLlawysgrif awdur wedi’i dderbyn, 182 KBTrwydded: 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.",

keywords = "permutation group, height of a permutation group, relational complexity, base size",

author = "Nick Gill and Bianca Lod{\`a}",

note = "Funding Information: The work of the first author was supported by EPSRC grant EP/R028702/1 . Publisher Copyright: {\textcopyright} 2021",

year = "2021",

month = nov,

day = "15",

doi = "10.1016/j.jalgebra.2021.10.037",

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T1 - Statistics for S acting on k-sets

AU - Gill, Nick

AU - Lodà, Bianca

PY - 2021/11/15

Y1 - 2021/11/15

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

U2 - 10.1016/j.jalgebra.2021.10.037

DO - 10.1016/j.jalgebra.2021.10.037

M3 - Article

VL - 00

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 00

M1 - S0021869321005366

ER -

Statistics for S acting on k-sets

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