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

Year 2020, , 271 - 287, 07.01.2020

Luca Amata Marilena Crupi

https://doi.org/10.24330/ieja.663094

Cited By: 2

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 homogeneous basis $g_1, \ldots, g_r$ such that $\deg g_1 \le \deg g_2 \le \cdots \le \deg g_r$. 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.

Keywords

Exterior algebra, Hilbert function, monomial submodule, lexicographic submodule

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