Abstract:
I will describe a bigraded Gorenstein ring, and certain Cohen-Macaulay subrings, that have Poincaré-Hilbert(-Frobenius) series described by major/descent generating functions of words on multisets, respectively standard Young tableaux. The calculation will naturally involve Ehrhart series of some polytopes; a classical identity of MacMahon-Carlitz will play an important role. A certain smoothing of the setup recovers the well-known coinvariant algebra; the Hilbert series formulae specialise to classical identities. There will be a final twist conjecturally involving a curious power of a Vandermonde matrix.