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Fixed point polynomials of permutation groups

Harden, CM and Penman, DB (2013) 'Fixed point polynomials of permutation groups.' Electronic Journal of Combinatorics, 20 (2). ISSN 1077-8926


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In this paper we study, given a group G of permutations of a finite set, the so-called fixed point polynomial ∑ in=0fixi, where fi is the number of permutations in G which have exactly i fixed points. In particular, we investigate how root location relates to properties of the permutation group. We show that for a large family of such groups most roots are close to the unit circle and roughly uniformly distributed round it. We prove that many families of such polynomials have few real roots. We show that many of these polynomials are irreducible when the group acts transitively. We close by indicating some future directions of this research.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: David Penman
Date Deposited: 15 May 2013 10:17
Last Modified: 23 Jun 2021 07:15

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