标题： 具有最小广义Barile-Macchia分解的单项式理想 显示英文标题

标题： Monomial ideals with minimal generalized Barile-Macchia resolutions

摘要： 我们识别出若干具有最小广义Barile-Macchia分解的单项式理想类。这些理想类包括一般的单项式理想、具有线性商的单项式理想以及超树的边理想。我们还刻画了其边理想为桥友好的连通单环图，并且特别地，这些理想具有最小的Barile-Macchia分解。Barile-Macchia和广义Barile-Macchia分解是细胞分解，也是特殊的Morse分解。 显示英文摘要

摘要： We identify several classes of monomial ideals that possess minimal generalized Barile-Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals with linear quotients, and edge ideals of hypertrees. We also characterize connected unicyclic graphs whose edge ideals are bridge-friendly and, in particular, have minimal Barile-Macchia resolutions. Barile-Macchia and generalized Barile-Macchia resolutions are cellular resolutions and special types of Morse resolutions.