The University of Michigan Combinatorics Seminar


Abstract 

We define the notion of a Hodge structure for a poset P, which is an action of S_{r+1} on the rchains of P, for all r. These actions must satisfy a certain condition relative to the usual boundary map on rchains. We show that under this condition, the homology of P admits the same kind of Hodge decomposition as does the Hochschild homology of a commutative algebra. As a specific example, we consider the poset of subsets of [nk] which have cardinality divisible by k. 