Cellular resolutions of ideals defined by nondegenerate simplicial homomorphisms

Benjamin Braun; Jonathan Browder; Steven Klee

doi:10.1007/s11856-012-0149-2

Cellular resolutions of ideals defined by nondegenerate simplicial homomorphisms

Benjamin Braun, Jonathan Browder, Steven Klee

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as homomorphism complexes. Motivated by work of Dochtermann and Engström, we introduce the class of cointerval simplicial complexes and investigate their combinatorial and topological properties. As a concrete illustration of these structural results, we introduce and study nonnesting monomial ideals, an interesting family of combinatorially defined ideals.

Original language	English
Pages (from-to)	321-344
Number of pages	24
Journal	Israel Journal of Mathematics
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s11856-012-0149-2
State	Published - Aug 2013

Bibliographical note

Funding Information:
∗ Benjamin Braun was partially supported by NSF award DMS-0758321. ∗∗ Jonathan Browder was partially supported by NSF VIGRE award DMS-0354131. † Steven Klee was partially supported by NSF VIGRE award DMS-0636297. Received February 11, 2011 and in revised form March 5, 2012

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s11856-012-0149-2

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author = "Benjamin Braun and Jonathan Browder and Steven Klee",

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N2 - In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as homomorphism complexes. Motivated by work of Dochtermann and Engström, we introduce the class of cointerval simplicial complexes and investigate their combinatorial and topological properties. As a concrete illustration of these structural results, we introduce and study nonnesting monomial ideals, an interesting family of combinatorially defined ideals.

AB - In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as homomorphism complexes. Motivated by work of Dochtermann and Engström, we introduce the class of cointerval simplicial complexes and investigate their combinatorial and topological properties. As a concrete illustration of these structural results, we introduce and study nonnesting monomial ideals, an interesting family of combinatorially defined ideals.

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Cellular resolutions of ideals defined by nondegenerate simplicial homomorphisms

Abstract

Bibliographical note

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