Let K be a field, V a K-vector space with basis e_1,..., e_n, and E the exterior algebra of V. To a given monomial ideal I di E we associate a special monomial ideal J with generators in the same degrees as those of I and such that the number of the minimal monomial generators in each degree of I and J coincide. We call J the colexsegment ideal associated to I. We prove that the class of strongly stable ideals in E generated in one degree satisfies the colex lower bound, that is, the total Betti numbers of the colexsegment ideal associated to a strongly stable ideal I di E generated in one degree are smaller than or equal to those of I.

Bounding betti numbers of monomial ideals in the exterior algebra

CRUPI, Marilena;FERRO', CARMELA
2015

Abstract

Let K be a field, V a K-vector space with basis e_1,..., e_n, and E the exterior algebra of V. To a given monomial ideal I di E we associate a special monomial ideal J with generators in the same degrees as those of I and such that the number of the minimal monomial generators in each degree of I and J coincide. We call J the colexsegment ideal associated to I. We prove that the class of strongly stable ideals in E generated in one degree satisfies the colex lower bound, that is, the total Betti numbers of the colexsegment ideal associated to a strongly stable ideal I di E generated in one degree are smaller than or equal to those of I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3095481
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