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Abstract
Given a finite group G acting on a set X let δk(G, X) denote the proportion of elements in G that have exactly k fixed points in X. Let Sn denote the symmetric group acting on [n] = { 1 , 2 , ⋯ , n} . For A⩽ Sm and B⩽ Sn , the permutational wreath product A≀ B has two natural actions and we give formulas for both, δk(A≀ B, [m] × [n]) and δk(A≀ B, [m] [n]) . We prove that for k= 0 the values of these proportions are dense in the intervals [δ(B, [n]) , 1] and [δ(A, [m]) , 1] . Among further results, we provide estimates for δ(G, [m] [n]) for subgroups G⩽ Sm≀ Sn containing Am[n] .
Original language | English |
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Pages (from-to) | 1-22 |
Number of pages | 22 |
Journal | Journal of Algebraic Combinatorics |
Volume | 59 |
Issue number | 1 |
Early online date | 28 Aug 2023 |
DOIs | |
Publication status | Published - Jan 2024 |
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Dive into the research topics of 'Derangements in wreath products of permutation groups'. Together they form a unique fingerprint.Projects
- 1 Finished
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Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. (Investigator 01) & Niemeyer, A. (Investigator 02)
ARC Australian Research Council
21/02/19 → 31/12/22
Project: Research