HILBERT FUNCTIONS OF GRADED MODULES OVER AN EXTERIOR ALGEBRA: AN ALGORITHMIC APPROACH

Let K be a field, E the exterior algebra of a finite dimensional K-vector space, and F a finitely generated graded free E-module with homogeneous basis g1, . . . , gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr. Given the Hilbert function of a graded E–module of the type F/M, with M graded submodule of F, the existence of the unique lexicographic submodule of F with the same Hilbert function as M is proved by a new algorithmic approach. Such an approach allows us to establish a criterion for determining if a sequence of nonnegative integers defines the Hilbert function of a quotient of a free E– module only via the combinatorial Kruskal–Katona’s theorem