Sequentially Cohen-Macaulay binomial edge ideals of closed graphs
Viviana Ene, Giancarlo Rinaldo, Naoki Terai
TL;DR
This paper characterizes when binomial edge ideals of closed graphs are sequentially Cohen-Macaulay using combinatorial methods and establishes an equivalence between approximate and almost Cohen-Macaulay properties for these ideals.
Contribution
It provides a complete combinatorial characterization of sequentially Cohen-Macaulay binomial edge ideals of closed graphs and links approximate Cohen-Macaulayness to almost Cohen-Macaulayness.
Findings
Characterization of sequentially Cohen-Macaulay binomial edge ideals for closed graphs
Equivalence between approximate and almost Cohen-Macaulay properties for these ideals
Complete combinatorial criteria for the Cohen-Macaulay properties
Abstract
In this paper we provide a full combinatorial characterization of sequentially Cohen-Macaulay binomial edge ideals of closed graphs. In addition, we show that a binomial edge ideal of a closed graph is approximately Cohen-Macaulay if and only if it is almost Cohen-Macaulay.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Polynomial and algebraic computation