Kruskal-Katona定理的推广

Pub Date : 2020-07-01 DOI:10.2478/auom-2020-0018

Luca Amata, M. Crupi

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引用次数: 4

摘要

抽象让K是一个字段,E有限维的外代数K向量空间,和F有限生成分级自由E-module均匀g1,。,gr这样度g1≤度g2≤···≤度gr。我们描述的希尔伯特功能分级E-modules类型的F / M M分级子模块的F F的存在的一个独特的词典子模块与希尔伯特函数一样起着至关重要的作用。

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A generalization of Kruskal–Katona’s theorem

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 g1, . . ., gr such that deg g1 ≤ deg g2 ≤ · · · ≤ deg gr. We characterize the Hilbert functions of graded E–modules of the type F/M, with M graded submodule of F. The existence of a unique lexicographic submodule of F with the same Hilbert function as M plays a crucial role.

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