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.

中文翻译：

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持久性模块之间的态射引起的持久性部分匹配

引入了持久部分匹配的概念，作为持久模块之间部分匹配的概括。我们研究了如何获得持久性部分匹配 $\mathcal{G}_f$ 和部分匹配 $\mathcal{M}_f$，由持久性模块之间的态射 $f$ 诱导，两者都是关于直接和的线性态射。还提供了它们的一些属性，包括它们在态射 $f$ 扰动后的稳定性，以及它们与 TDA 中已经定义的其他诱导部分匹配的关系。