Let I be the ideal generated by alternating polynomials in two sets of n variables. Haiman proved that the q, t-Catalan number is the Hilbert series of the bi-graded vector space M(= ⊕ d1,d2 Md1,d2) spanned by a minimal set of generators for I. In this paper we give simple upper bounds on dim Md1,d2 in terms of number of partitions, and find all bi-degrees… (More)