Irredundant bases for the symmetric group

Colva Roney-Dougal, Peiran Wu*

*Corresponding author for this work

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An irredundant base of a group 𝐺 acting faithfully on a finite set Ξ“ is a sequence of points in Ξ“ that produces a strictly descending chain of pointwise stabiliser sub-groups in 𝐺,terminating at the trivial subgroup. Suppose that 𝐺 is S𝑛 or A𝑛 acting primitively on Ξ“, and that the point stabiliser is primitive in its natural action on𝑛points. We prove that the maximum size of an irredundant base of 𝐺 is 𝑂 (βˆšπ‘›),and in most cases 𝑂((log𝑛)2). We also show that these bounds are best possible.
Original languageEnglish
Number of pages15
JournalBulletin of the London Mathematical Society
VolumeEarly View
Early online date20 Mar 2024
Publication statusE-pub ahead of print - 20 Mar 2024


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