论文标题
零件中的整体：将$ n $ d的持久性模块放入不可兼容的$（n + 1）$ D
The Whole in the Parts: Putting $n$D Persistence Modules Inside Indecomposable $(n + 1)$D Ones
论文作者
论文摘要
已经提出了多维持久性来研究由多个参数索引的数据中拓扑特征的持久性。在这项工作中，我们从较高维度不可分解的持久性模块的角度的角度进一步探索了其代数并发症，其中包含较低维度的模块作为超平面限制。我们以前的工作进行了建设性的表明，任何有限的矩形解释$ n $ d持久模块都是对某些不可分解的$（n+1）$ d持久模块的超平面限制，这是$ n = 1 $的结果的推论。在这里，我们通过删除矩形解释性的要求来扩展这一点。此外，在基础字段是可数的情况下，我们构建了一个不可或缺的$（n+1）$ d持久模块，其中包含所有$ n $ d持久模块，直至同构，作为超平面限制。最后，在$ n = 1 $的情况下，我们提出了一种最小的结构，可以改善我们以前的建筑。
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher dimensional indecomposable persistence modules containing lower dimensional ones as hyperplane restrictions. Our previous work constructively showed that any finite rectangle-decomposable $n$D persistence module is the hyperplane restriction of some indecomposable $(n+1)$D persistence module, as a corollary of the result for $n=1$. Here, we extend this by dropping the requirement of rectangle-decomposability. Furthermore, in the case that the underlying field is countable, we construct an indecomposable $(n+1)$D persistence module containing all $n$D persistence modules, up to isomorphism, as hyperplane restrictions. Finally, in the case $n=1$, we present a minimal construction that improves our previous construction.
