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The cycle polynomial of a permutation group
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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 | 252130100 | |
dc.identifier | 9c005015-45e4-4405-9166-1461765e8204 | |
dc.identifier | 85042212781 | |
dc.identifier | 000432156200009 | |
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 | ORCID: /0000-0003-3130-9505/work/58055707 | |
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.format.extent | 276871 | |
dc.language.iso | eng | |
dc.relation.ispartof | Electronic Journal of Combinatorics | 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.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 |
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