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 homo- geneous basis g_1,...., g_r such that deg g_1= deg g_2= ...= deg g_r. Given the Hilbert function of a graded E-module of the type F=M, with M graded sub- module 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.

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

Amata, Luca
Writing – Original Draft Preparation
;
Crupi, Marilena
Writing – Original Draft Preparation
2020-01-01

Abstract

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 homo- geneous basis g_1,...., g_r such that deg g_1= deg g_2= ...= deg g_r. Given the Hilbert function of a graded E-module of the type F=M, with M graded sub- module 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.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3150006
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