巴里勒-马奇亚决议

Pub Date : 2024-02-05 DOI:10.1007/s10801-023-01293-9

Trung Chau, Selvi Kara

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引用次数: 0

摘要

我们通过离散莫尔斯理论构建单项式理想的蜂窝解析。特别是，我们开发了一种创建同质非循环匹配的算法，并将这些匹配诱导出的单元解析称为巴里勒-麦奇亚解析。对于加权定向森林的边理想和（大多数）循环，这些决议都是最小的。因此，我们提供了分级贝蒂数和投影维数的递推公式。此外，我们还将巴里勒-麦基雅解析与巴齐斯和韦尔克创建的解析以及一些著名的简单解析进行了比较。在某些假设条件下，只要上述决议是最小的，巴里勒-马奇亚决议也是最小的。

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Barile–Macchia resolutions

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Barile–Macchia resolutions

We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we develop an algorithm to create homogeneous acyclic matchings and we call the cellular resolutions induced from these matchings Barile–Macchia resolutions. These resolutions are minimal for edge ideals of weighted oriented forests and (most) cycles. As a result, we provide recursive formulas for graded Betti numbers and projective dimension. Furthermore, we compare Barile–Macchia resolutions to those created by Batzies and Welker and some well-known simplicial resolutions. Under certain assumptions, whenever the above resolutions are minimal, so are Barile–Macchia resolutions.

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