article epub_ahead yes Rocio Gonzalez-Diaz author Manuel Soriano Trigueros author 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea80000-0003-2449-1433 Alvaro Torras-Casas author HeEd department 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. https://creativecommons.org/licenses/by/4.0/ Elsevier2026 eng Persistence modulePersistence mapPersistent homology 0747-7171 1095-855X 2006.1110010.1016/j.jsc.2026.102598 138 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> Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598. 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> R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic Computation 138 (2026). 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>. 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>. 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. 222912026-07-13T09:43:38Z2026-07-13T12:00:07Z