Cycle indices and subgroup lattices

Christopher D. Wensley; Ifor Morris

doi:10.1016/0012-365X(93)90060-7

Cycle indices and subgroup lattices

Christopher D. Wensley
, Ifor Morris

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

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We determine the properties of the conjugate of a diagonal function \Delta by the mark function in the incidence algebra of the poset of conjugacy classes of subgroups of a finite group G. Particular choices for \Delta provide applications to the Burnside ring of G, to the theory of \beta-rings and to Redfield-Polya enumeration. In particular, we obtain a Polya-like substitution formula for the K[J]-inventory of colourings of a set whose symmetry group is a wreath product G[F].

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	173-195
Cyfnodolyn	Discrete Mathematics
Cyfrol	118
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1016/0012-365X(93)90060-7
Statws	Cyhoeddwyd - 1993

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10.1016/0012-365X(93)90060-7Trwydded: !!Other

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@article{0facb2a63ac640eaac290c51eaa2be3c,

title = "Cycle indices and subgroup lattices",

abstract = "We determine the properties of the conjugate of a diagonal function \textbackslash{}Delta by the mark function in the incidence algebra of the poset of conjugacy classes of subgroups of a finite group G. Particular choices for \textbackslash{}Delta provide applications to the Burnside ring of G, to the theory of \textbackslash{}beta-rings and to Redfield-Polya enumeration. In particular, we obtain a Polya-like substitution formula for the K[J]-inventory of colourings of a set whose symmetry group is a wreath product G[F]. ",

author = "Wensley, \{Christopher D.\} and Ifor Morris",

year = "1993",

doi = "10.1016/0012-365X(93)90060-7",

language = "English",

volume = "118",

pages = "173--195",

journal = "Discrete Mathematics",

issn = "1872-681X",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Cycle indices and subgroup lattices

AU - Wensley, Christopher D.

AU - Morris, Ifor

PY - 1993

Y1 - 1993

N2 - We determine the properties of the conjugate of a diagonal function \Delta by the mark function in the incidence algebra of the poset of conjugacy classes of subgroups of a finite group G. Particular choices for \Delta provide applications to the Burnside ring of G, to the theory of \beta-rings and to Redfield-Polya enumeration. In particular, we obtain a Polya-like substitution formula for the K[J]-inventory of colourings of a set whose symmetry group is a wreath product G[F].

AB - We determine the properties of the conjugate of a diagonal function \Delta by the mark function in the incidence algebra of the poset of conjugacy classes of subgroups of a finite group G. Particular choices for \Delta provide applications to the Burnside ring of G, to the theory of \beta-rings and to Redfield-Polya enumeration. In particular, we obtain a Polya-like substitution formula for the K[J]-inventory of colourings of a set whose symmetry group is a wreath product G[F].

U2 - 10.1016/0012-365X(93)90060-7

DO - 10.1016/0012-365X(93)90060-7

M3 - Article

SN - 1872-681X

VL - 118

SP - 173

EP - 195

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

Cycle indices and subgroup lattices

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