<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>K</italic> be a field, <italic>E</italic> the exterior algebra of a finite dimensional <italic>K-</italic>vector space, and <italic>F</italic> a finitely generated graded free <italic>E</italic>-module with homogeneous basis <italic>g</italic>1, . . ., <italic>gr</italic> such that deg <italic>g</italic>1 ≤ deg <italic>g</italic>2 ≤ · · · ≤ deg <italic>gr</italic>. We characterize the Hilbert functions of graded <italic>E</italic>–modules of the type <italic>F/M</italic>, with <italic>M</italic> graded submodule of <italic>F</italic>. The existence of a unique lexicographic submodule of <italic>F</italic> with the same Hilbert function as <italic>M</italic> plays a crucial role.</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.

A generalization of Kruskal–Katona’s theorem

Department of Mathematics and Computer Sciences, Physics and Earth Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A generalization of Kruskal\u2013Katona\u2019s theorem"}

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, . ....

A generalization of Kruskal–Katona’s theorem

Published Online: Sep 22, 2020

Page range: 35 - 51

Received: Jul 10, 2019

Accepted: Sep 24, 2019

DOI: https://doi.org/10.2478/auom-2020-0018

Keywords
Exterior algebra, Hilbert functions, Monomial submodules, lexicographic submodules

© 2020 Luca Amata et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A generalization of Kruskal–Katona’s theorem

Published Online: Sep 22, 2020

Page range: 35 - 51

Received: Jul 10, 2019

Accepted: Sep 24, 2019

DOI: https://doi.org/10.2478/auom-2020-0018

KeywordsExterior algebra, Hilbert functions, Monomial submodules, lexicographic submodules

© 2020 Luca Amata et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Exterior algebra, Hilbert functions, Monomial submodules, lexicographic submodules