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Fixed Point Polynomials of Permutation Groups

Harden, CM and Penman, DB (2013) 'Fixed Point Polynomials of Permutation Groups.' The Electronic Journal of Combinatorics, 20 (2). ISSN 1077-8926

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Abstract

<jats:p>In this paper we study, given a group $G$ of permutations of a finite set, the so-called fixed point polynomial $\sum_{i=0}^{n}f_{i}x^{i}$, where $f_{i}$ 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. A corrigendum was appended to this paper on 10th October 2014. </jats:p>

Item Type: Article
Uncontrolled Keywords: group theory; finite permutation groups
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 15 May 2013 10:17
Last Modified: 15 Jan 2022 00:34
URI: http://repository.essex.ac.uk/id/eprint/6185

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