Minimal Cohen-Macaulay Simplicial Complexes
Combinatorics
2019-05-14 v1 Commutative Algebra
Abstract
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen-Macaulay. We show that many interesting examples of Cohen-Macaulay complexes in combinatorics are minimal, including Rudin's ball, Ziegler's ball, the dunce hat, and recently discovered non-partitionable Cohen-Macaulay complexes. We further provide various ways to construct such complexes.
Keywords
Cite
@article{arxiv.1905.05043,
title = {Minimal Cohen-Macaulay Simplicial Complexes},
author = {Hailong Dao and Joseph Doolittle and Justin Lyle},
journal= {arXiv preprint arXiv:1905.05043},
year = {2019}
}