The minimum length of a base for the symmetric group acting on partitions

Carmit Benbenishty; Jonathan A. Cohen; Alice C. Niemeyer

doi:10.1016/j.ejc.2006.08.014

The minimum length of a base for the symmetric group acting on partitions

Carmit Benbenishty^*, Jonathan A. Cohen, Alice C. Niemeyer

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible.

Original language	English
Pages (from-to)	1575-1581
Number of pages	7
Journal	European Journal of Combinatorics
Volume	28
Issue number	6
DOIs	https://doi.org/10.1016/j.ejc.2006.08.014
Publication status	Published - Aug 2007
Externally published	Yes

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title = "The minimum length of a base for the symmetric group acting on partitions",

abstract = "A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible.",

author = "Carmit Benbenishty and Cohen, {Jonathan A.} and Niemeyer, {Alice C.}",

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AU - Benbenishty, Carmit

AU - Cohen, Jonathan A.

AU - Niemeyer, Alice C.

PY - 2007/8

Y1 - 2007/8

N2 - A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible.

AB - A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible.

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U2 - 10.1016/j.ejc.2006.08.014

DO - 10.1016/j.ejc.2006.08.014

M3 - Article

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SP - 1575

EP - 1581

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 6

ER -

The minimum length of a base for the symmetric group acting on partitions

Abstract

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