---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22291'
abstract:
- lang: eng
  text: Persistent homology is a fundamental tool in Topological Data Analysis. The
    associated algebraic structure is the persistence module, a sequence of vector
    spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute
    invariant known as the persistence diagram. However, this is no longer the case
    for maps between persistence modules (i.e. persistence maps). We propose a new
    invariant for persistence maps, consisting of a partial matching between the persistence
    diagrams of the domain and codomain modules. We show that this invariant is additive
    with respect to the direct sum decomposition of persistence maps, is more discriminative
    than the image module, and is computable in cubic time. Furthermore, we provide
    an implementation and demonstrate its efficiency by integrating it with edge collapse
    techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical
    contribution, we describe how to induce a persistence map between two flag complexes
    that have been independently simplified via edge collapses, even when a direct
    simplicial map between them is no longer available.
acknowledgement: This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR,
  under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant
  CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting
  this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also
  like to thank Lars M Salbu for fruitful discussions regarding the operators from
  Definition 4.1 and their relation with the order relations introduced in Definition
  3.2.
article_number: '102598'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rocio
  full_name: Gonzalez-Diaz, Rocio
  last_name: Gonzalez-Diaz
- first_name: Manuel
  full_name: Soriano Trigueros, Manuel
  id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
  last_name: Soriano Trigueros
  orcid: 0000-0003-2449-1433
- first_name: Alvaro
  full_name: Torras-Casas, Alvaro
  last_name: Torras-Casas
citation:
  ama: Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings
    induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138.
    doi:<a href="https://doi.org/10.1016/j.jsc.2026.102598">10.1016/j.jsc.2026.102598</a>
  apa: Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive
    partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.jsc.2026.102598">https://doi.org/10.1016/j.jsc.2026.102598</a>
  chicago: Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas.
    “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic
    Computation</i>. Elsevier, 2026. <a href="https://doi.org/10.1016/j.jsc.2026.102598">https://doi.org/10.1016/j.jsc.2026.102598</a>.
  ieee: R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial
    matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>,
    vol. 138. Elsevier, 2026.
  ista: Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial
    matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.
  mla: Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence
    Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026,
    doi:<a href="https://doi.org/10.1016/j.jsc.2026.102598">10.1016/j.jsc.2026.102598</a>.
  short: R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic
    Computation 138 (2026).
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: The code used for the computational experiments is available
  in https://github.com/Cimagroup/IBloFunMatch
date_created: 2026-07-13T09:43:38Z
date_published: 2026-06-23T00:00:00Z
date_updated: 2026-07-13T12:00:07Z
day: '23'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2026.102598
external_id:
  arxiv:
  - '2006.11100'
fulldoi: https://doi.org/10.1016/j.jsc.2026.102598
has_accepted_license: '1'
intvolume: '       138'
keyword:
- Persistence module
- Persistence map
- Persistent homology
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1016/j.jsc.2026.102598
mathsc:
- 55N31
- 16G20
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Symbolic Computation
publication_identifier:
  eissn:
  - 1095-855X
  issn:
  - 0747-7171
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: no
title: Additive partial matchings induced by persistence maps
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 138
year: '2026'
...