论文标题
$ \ mathbb {a} _n $ Quiver的持久性和稳定性
Persistence and Stability of the $\mathbb{A}_n$ Quiver
论文作者
论文摘要
我们为锯齿形持久模块介绍了两个新的距离。第一个使用Auslander-Reiten Quiver理论，第二个是经典交织距离的扩展。两者都是在$ \ Mathbb {a} _n $ Quiver的完全一般方向上定义的。我们比较了M. Botnan和M. Lesnick引入的第一个距离与块沿纯曲折方向的两者（作为瓶颈距离）之间的完整尖锐的Lipschitz边界。纸的最后部分提出了延长的交织距离所必需的尖锐的Lipschitz边界，以支配从Auslander-Reiten Quiver产生的距离。这些界限是为$ \ mathbb {a} _n $ Quiver的一般方向而获得的。
We introduce two new distances for zigzag persistence modules. The first uses Auslander-Reiten quiver theory, and the second is an extension of the classical interleaving distance. Both are defined over completely general orientations of the $\mathbb{A}_n$ quiver. We compare the first distance to the block distance introduced by M. Botnan and M. Lesnick and obtain the full set of sharp Lipschitz bounds between the two (as bottleneck distances) over pure zigzag orientations. The final portion of the paper presents sharp Lipschitz bounds necessary for the extended interleaving distance to dominate the distance that is created from the Auslander-Reiten quiver. These bounds are obtained for general orientations of the $\mathbb{A}_n$ quiver.
