Cycle indices and subgroup lattices
Research output: Contribution to journal › Article › peer-review
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In: Discrete Mathematics, Vol. 118, 1993, p. 173-195.
Research output: Contribution to journal › Article › peer-review
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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
VL - 118
SP - 173
EP - 195
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 1872-681X
ER -