Persistence Partial Matchings Induced by Morphisms between Persistence Modules

The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is introduced. We study how to obtain a persistence partial matching $\mathcal{G}_f$, and a partial matching $\mathcal{M}_f$, induced by a morphism $f$ between persistence modules, both being linear with respect to direct sums of morphisms. Some of their properties are also provided, including their stability after a perturbation of the morphism $f$, and their relationship with other induced partial matchings already defined in TDA.