Powers of $t$-spread principal Borel ideals

TL;DR

This paper investigates the algebraic properties of $t$-spread principal Borel ideals, proving they are sequentially Cohen-Macaulay, analyzing their powers, and exploring their depth and persistence properties.

Contribution

It establishes that $t$-spread principal Borel ideals are sequentially Cohen-Macaulay and studies their powers and depth behavior, which was previously unexplored.

Findings

Proved $t$-spread principal Borel ideals are sequentially Cohen-Macaulay.

Showed these ideals have the strong persistence property.

Computed the limit depth of these ideals.

Abstract

We prove that $t$-spread principal Borel ideals are sequentially Cohen-Macaulay and study their powers. We show that these ideals possess the strong persistence property and compute their limit depth.