Files in this item
The cycle polynomial of a permutation group
Item metadata
dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Semeraro, Jason | |
dc.date.accessioned | 2018-03-02T16:30:05Z | |
dc.date.available | 2018-03-02T16:30:05Z | |
dc.date.issued | 2018-01-25 | |
dc.identifier.citation | Cameron , P J & Semeraro , J 2018 , ' The cycle polynomial of a permutation group ' , Electronic Journal of Combinatorics , vol. 25 , no. 1 , P1.14 . < http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p14 > | en |
dc.identifier.issn | 1077-8926 | |
dc.identifier.other | PURE: 252130100 | |
dc.identifier.other | PURE UUID: 9c005015-45e4-4405-9166-1461765e8204 | |
dc.identifier.other | Scopus: 85042212781 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/58055707 | |
dc.identifier.other | WOS: 000432156200009 | |
dc.identifier.uri | https://hdl.handle.net/10023/12840 | |
dc.description.abstract | The cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles.In the first part of the paper, we develop basic properties of this polynomial, and give a number of examples. In the 1970s, Richard Stanley introduced the notion of reciprocity for pairs of combinatorial polynomials. We show that, in a considerable number of cases, there is a polynomial in the reciprocal relation to the cycle polynomial of G; this is the orbital chromatic polynomial of Γ and G, where Γ is a G-invariant graph, introduced by the first author, Jackson and Rudd. We pose the general problem of finding all such reciprocal pairs, and give a number of examples and characterisations: the latter include the cases where Γ is a complete or null graph or a tree. The paper concludes with some comments on other polynomials associated with a permutation group. | |
dc.format.extent | 13 | |
dc.language.iso | eng | |
dc.relation.ispartof | Electronic Journal of Combinatorics | en |
dc.rights | Copyright (c)2017 the authors. This work is made available online in accordance with the publisher’s policies. This is the final published version of the work which was originally published at http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p14 | en |
dc.subject | Permutation group | en |
dc.subject | Chromatic polynomial | en |
dc.subject | Reciprocity | en |
dc.subject | QA Mathematics | en |
dc.subject | Mathematics(all) | en |
dc.subject | NDAS | en |
dc.subject.lcc | QA | en |
dc.title | The cycle polynomial of a permutation group | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p14 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.