On fixed points of permutations

By Persi Diaconis, Jason E. Fulman, Robert M. Guralnick. 2007

52 citations recorded by the source corpus.

The number of fixed points of a random permutation of {1,2,…,n} has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they are trivial – almost every permutation has no fixed points. For the usual action of the symmetric group on k-sets of {1,2,…,n}, the limit is a polynomial in independent Poisson variables. This exhausts all cases. We obtain asymptotic estimates in some examples, and give a survey of related results.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/279374a861a75985be27fd14bbec13f4c49d5990

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jason E. Fulman
2. Robert M. Guralnick
3. Aner Shalev

In Discrete Mathematics and Combinatorics

1. Jason E. Fulman
2. Robert M. Guralnick
3. Sourav Chatterjee
4. Aner Shalev
5. Peter J. Cameron
6. Martin W. Liebeck

In Mathematical Physics

1. Robert M. Guralnick
2. Jason E. Fulman
3. Sourav Chatterjee
4. Jim Pitman
5. Kent E. Morrison

Citations in the corpus

• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (2009, background): “The Boston-Shalev conjecture was proved for alternating and symmetric groups in [LuP]. See also [D], [ DFG ], and [FG3].”