Monomial ideals with minimal generalized Barile-Macchia resolutions
Trung Chau, Huy Tai Ha, Aryaman Maithani
TL;DR
This paper identifies classes of monomial ideals with minimal generalized Barile-Macchia resolutions, including generic ideals, ideals with linear quotients, and edge ideals of hypertrees, expanding understanding of cellular Morse resolutions.
Contribution
It characterizes specific classes of monomial ideals and graphs that admit minimal generalized Barile-Macchia resolutions, providing new insights into their structure.
Findings
Identified classes of monomial ideals with minimal resolutions
Characterized connected unicyclic graphs with bridge-friendly edge ideals
Expanded understanding of cellular Morse resolutions
Abstract
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.
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