lambda-operations in beta-rings
Research output: Contribution to journal › Article › peer-review
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.
| Original language | English |
|---|---|
| Pages (from-to) | 247-267 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Volume | 121 |
| Publication status | Published - 1997 |