TY - JOUR

T1 - lambda-operations in beta-rings

AU - Wensley, Christopher D.

AU - Morris, Ifor

PY - 1997

Y1 - 1997

N2 - A beta-ring is supplied with operations beta_H where H runs over the conjugacy classes of subgroups of the symmetric group S_n. In an earlier paper we introduced a second set of operations lambda_H and we show here that the two sets are related by the isomorphism beta_H(-X) = (-1)^n lambda_H(X). We then consider the operations beta_H and lambda_H as combinatorial species, in the sense of Joyal, and express their molecular decomposition as a finite sum of products of the exponential species of degree at most n. We give combinatorial interpretations for beta_{S_n}-structures and lambda_{S_n}-structures and derive various species isomorphisms.

AB - A beta-ring is supplied with operations beta_H where H runs over the conjugacy classes of subgroups of the symmetric group S_n. In an earlier paper we introduced a second set of operations lambda_H and we show here that the two sets are related by the isomorphism beta_H(-X) = (-1)^n lambda_H(X). We then consider the operations beta_H and lambda_H as combinatorial species, in the sense of Joyal, and express their molecular decomposition as a finite sum of products of the exponential species of degree at most n. We give combinatorial interpretations for beta_{S_n}-structures and lambda_{S_n}-structures and derive various species isomorphisms.

M3 - Article

VL - 121

SP - 247

EP - 267

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 1469-8064

ER -