Principal vector-spread Borel ideals

TL;DR

This paper investigates a specific class of squarefree Borel ideals, providing their primary decomposition, proving they are sequentially Cohen-Macaulay, and classifying when their ordinary and symbolic powers are equal.

Contribution

It introduces and analyzes principal vector-spread Borel ideals, offering explicit primary decompositions and a complete classification of power equality conditions.

Findings

Computed minimal primary decompositions.

Proved ideals are sequentially Cohen-Macaulay.

Classified ideals with equal ordinary and symbolic powers.

Abstract

We study the class of squarefree principal vector-spread Borel ideals. We compute the minimal primary decomposition of these ideals and thereby we prove that they are sequentially Cohen-Macaulay. As the final conclusion of our results, we completely classify the ideals in our class having the property that their ordinary and symbolic powers coincide.