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λ-Operations in β-rings

Published online by Cambridge University Press:  01 March 1997

I. MORRIS  and
C. D. WENSLEY
I. MORRIS
Affiliation:
School of Mathematics, University of Wales, Bangor, Gwynedd LL57 1UT
C. D. WENSLEY
Affiliation:
School of Mathematics, University of Wales, Bangor, Gwynedd LL57 1UT
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Abstract

A β-ring is supplied with operations βH where Hruns over the conjugacy classes of subgroups of the symmetric groups Sn. In an earlier paper we introduced a second set of operations λH and we show here that the two sets are related by the isomorphism

formula here

We then consider the operations βH and λH as combinatorial species, in the sense of Joyal, and express their molecular decomposition as a finite sum of products of the exponential species with molecular species of degree at most n. We give combinatorial interpretations for βSn-structures and λSn-structures and derive various species isomorphisms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 247 - 267
Copyright
© Cambridge Philosophical Society 1997

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