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.

翻译：采用持久性部分匹配的概念,作为持久性模块之间部分匹配的概括性概念。我们研究如何获得持久性部分匹配$\ mathcal{G ⁇ ff$,和部分匹配$\mathcal{M ⁇ f$,由持久性模块之间形态化的美元引起的部分匹配$\mathcal{M ⁇ f$,两者在形态化的直接金额方面都是线性。他们的一些属性也得到了提供,包括形态化干扰后的稳定性$f$,以及他们与TDA中已经定义的其他诱导性部分匹配的关系。