Regularity of quasi-symbolic and bracket powers of Borel type ideals

TL;DR

This paper investigates the regularity properties of quasi-symbolic and bracket powers of Borel type monomial ideals, establishing bounds and relations that enhance understanding of their algebraic structure.

Contribution

It provides new bounds and relations for the regularity of quasi-symbolic and bracket powers of Borel type ideals, advancing algebraic theory.

Findings

reg(I^{((q))}) q q  reg(I)

reg(I^{[q]}) q q  reg(I)

An upper bound for reg(I^{[q]})

Abstract

In this paper, we show that the regularity of the q-th quasi-symbolic power $I^{((q))}$ and the regularity of the $q$-th bracket power $I^{[q]}$ of a monomial ideal of Borel type $I$, satisfy the relations $reg(I^{((q))})\leq q \cdot reg(I)$, respectively $reg(I^{[q]})\geq q\cdot reg(I)$. Also, we give an upper bound for $reg(I^{[q]})$.