Abstract

this paper we consider the Sn -representation on the homology of certain Cohen-Macaulay subposets of \Pi n : In Section 1, we present a general technique for manipulating these homology modules. The unique properties of the partition lattice allow further simplification of these formulas, culminating in plethystic generating functions which, by recursive computation, yield the Frobenius characteristic of the representation. We illustrate our technique by giving simple derivations of three known formulas: 1. a formula for the plethystic inverse of the sum of the cycle indicators of the symmetric groups; this is essentially equivalent to Cadogan's formula; 2. a plethystic formula which determines the characteristic of the homology representation on the lattice \Pi

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