Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology
type: Item
instance of: scholarly article
title: Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology
author: Sara Scaramuccia
author: C. Landi
published in: Journal of Combinatorial Optimization
publication date: 2022-10-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1904.05081
review text: The goal of the paper under review is to develop techniques to ease multi-parameter persistence computations. Inspired by the success of discrete Morse theory as a tool to preprocess in the classical persistence, the authors introduce the notion of a relative-perfect discrete gradient vector field. The authors prove that a relative-perfect discrete gradient vector field has the least number of critical cells for multi-parameter persistence, the natural extension of the defining property of perfect discrete Morse functions. The authors further show a generalization of the classical discrete Morse inequalities by considering a filtration structure. This yields a pair of inequalities by using the number of critical cells to bound the Betti tables of persistence modules.
reviewed by: Nicholas A. Scoville
Mathematics Subject Classification ID: 55N31
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 37B35
Mathematics Subject Classification ID: 13D02
zbMATH DE Number: 7603271
zbMATH Keywords: multiparameter persistent homology
zbMATH Keywords: discrete Morse theory
zbMATH Keywords: persistence modules
zbMATH Keywords: Betti tables
zbMATH Keywords: Morse inequalities
MaRDI profile type: Publication
OpenAlex ID: W3156776635
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DOI: 10.1007/S10878-021-00729-X
description: scientific article; zbMATH DE number 7603271