Computing derangement probabilities of the symmetric group acting on\n k-sets

2015/11/12 by John R. Britnell, Mark Wildon, Britnell, John R. +1
Computer Science · Mathematics · #05A05 #20B30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #secondary: 05A17 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1511.04106

openalex publication_date 2015/11/12 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let i(\∞,k) be the limiting proportion, as n \→ \∞, of\npermutations in the symmetric group of degree n that fix a k-set. We give\nan algorithm for computing i(\∞,k) and state the values of i(\∞,k)\nfor k \≤ 30. These values are consistent with a conjecture of Peter Cameron\nthat i(\∞,k) is a decreasing function of k.\n

Related

• The Probability of Generating the Symmetric Group
• Derangements in wreath products of permutation groups
• Derangements in finite classical groups and characteristic polynomials of random matrices
• The probability of generating the symmetric group with a commutator condition
• The inversion statistic in derangements and in other permutations with a prescribed number of fixed points