Set superpartitions and superspace duality modules

The superspace ring omega(n) is a rank n polynomial ring tensored with a rank n exterior algebra. Using an extension of the Vandermonde determinant to omega(n), the authors previously defined a family of doubly graded quotients W-n,W-k of omega(n), which carry an action of the symmetric group S-n and satisfy a bigraded version of Poincar & eacute; Duality. In this paper, we examine the duality modules W-n,W-k in greater detail. We describe a monomial basis of W-n,W-k and give combinatorial formulas for its bigraded Hilbert and Frobenius series. These formulas involve new combinatorial