Projects per year
Abstract
Given a finite group G acting on a set X let δ_{k}(G, X) denote the proportion of elements in G that have exactly k fixed points in X. Let S_{n} denote the symmetric group acting on [n] = { 1 , 2 , ⋯ , n} . For A⩽ S_{m} and B⩽ S_{n} , the permutational wreath product A≀ B has two natural actions and we give formulas for both, δ_{k}(A≀ B, [m] × [n]) and δ_{k}(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⩽ S_{m}≀ S_{n} containing Am[n] .
Original language  English 

Pages (fromto)  122 
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 
Projects
 1 Finished

Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. & Niemeyer, A.
21/02/19 → 31/12/22
Project: Research