论文标题
Barile-Macchia决议
Barile-Macchia resolutions
论文作者
论文摘要
我们通过离散的莫尔斯理论构建单个理想的细胞分辨率。特别是，我们开发了一种算法来创建均匀的无环匹配，我们称这些匹配型barile-macchia分辨率引起的细胞分辨率。对于加权定向森林和（大多数）周期的边缘理想，这些分辨率是最小的。结果，我们为分级的贝蒂数字和投影维度提供递归公式。此外，我们将Barile-Macchia的决议与蝙蝠侠和韦尔克以及一些众所周知的简单决议所创造的决议进行了比较。在某些假设下，每当上述决议最少时，Barile-Macchia决议也是如此。
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.
