Minimal cellular resolutions of the edge ideals of forests
type: Item
instance of: scholarly article
title: Minimal cellular resolutions of the edge ideals of forests
zbMATH Open document ID: 1472.13012
DOI: 10.37236/8810
author: Margherita Barile
author: Antonio Macchia
published in: The Electronic Journal of Combinatorics
publication date: 2020-06-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1902.02740
review text: The authors consider edge ideals of forests and give an explicit construction of a cellular resolution that is minimal. Their minimal resolution is based on the Lyubeznik resolution and on the discrete Morse theory. They present a procedure for selecting the admissible symbols which generate the free modules of the resolution. In the end of the paper, they compute the graded Betti numbers and the projective dimension.
reviewed by: Anda-Georgina Olteanu
Mathematics Subject Classification ID: 13A70
Mathematics Subject Classification ID: 13F65
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 7208439
zbMATH Keywords: cellular resolution
zbMATH Keywords: Morse theory
zbMATH Keywords: edge ideal
zbMATH Keywords: Betti numbers
describes a project that uses: CoCoA
describes a project that uses: CoCoALib
MaRDI profile type: Publication
OpenAlex ID: W3032509926
arXiv ID: 1902.02740
cites work: Pruned cellular free resolutions of monomial ideals
cites work: Cellular resolutions of monomial modules
cites work: Discrete Morse theory for cellular resolutions
cites work: On discrete Morse functions and combinatorial decompositions
cites work: Cellular resolutions of cointerval ideals
cites work: Multigraded Betti numbers of simplicial forests
cites work: Cellular resolutions of Cohen-Macaulay monomial ideals
cites work: Morse theory for cell complexes
cites work: Linear resolutions of quadratic monomial ideals
cites work: Non-vanishingness of Betti numbers of edge ideals
cites work: A new explicit finite free resolution of ideals generated by monomials in an R-sequence
cites work: The Eliahou-Kervaire resolution is cellular
cites work: Three simplicial resolutions
cites work: Q5462454
cites work: Lyubeznik's resolution and rooted complexes
cites work: Computing the Betti table of a monomial ideal: a reduction algorithm
description: scientific article