Classification of Cohen-Macaulay $t$-spread lexsegment ideals via simplicial complexes

TL;DR

This paper investigates the structure of Cohen-Macaulay $t$-spread lexsegment ideals using simplicial complexes, providing a classification and analyzing algebraic invariants of these ideals.

Contribution

It offers a complete classification of Cohen-Macaulay $t$-spread lexsegment ideals and explores their algebraic invariants through simplicial complexes.

Findings

Classified all Cohen-Macaulay $t$-spread lexsegment ideals.

Determined algebraic invariants of $t$-spread lexsegment ideals.

Analyzed minimal primary decompositions via simplicial complexes.

Abstract

We study the minimal primary decomposition of completely $t$-spread lexsegment ideals via simplicial complexes. We determine some algebraic invariants of such a class of $t$-spread ideals. Hence, we classify all $t$-spread lexsegment ideals which are Cohen-Macaulay.