The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers
Year: 2021
Type: preprint
Abstract: We show that the generalized persistence diagram by Kim and M\'emoli encodes the bigraded Betti numbers of finite $2$-parameter persistence modules. More interestingly, the way to read off the bigraded Betti numbers from the generalized persistence diagram is parallel to how the bigraded Betti numbers are extracted from interval decomposable modules. Our results implies that all invariants of 2-parameter persistence modules that are computed by the software RIVET are encoded in the generalized persistence diagram. Along the way, we verify that an invariant of finite 2-parameter persistence modules that was recently introduced by Asashiba et al. also encodes the bigraded Betti numbers.
Source: arXiv (Cornell University)
Authors: Woojin Kim, Samantha Moore
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3208680489