Enumeration of Concave Integer Partitions

An integer partition ‚‘ n corresponds, via its Ferrers diagram, to an artinian monomial ideal I ‰ C[x;y] with dimC C[x;y]=I = n. If ‚ corresponds to an integrally closed ideal we call itconcave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts. 1. concave partitions