Freiman Borel type ideals

TL;DR

This paper classifies specific classes of Borel type monomial ideals, including Borel and principal k-Borel ideals, that satisfy a particular algebraic equality characterizing Freiman ideals, expanding understanding of their structure.

Contribution

It provides a classification of certain Borel type ideals that are Freiman, including those with multiple Borel generators and principal k-Borel ideals.

Findings

Classified Borel ideals that are Freiman.

Identified conditions for principal k-Borel ideals to be Freiman.

Extended the understanding of algebraic properties of Borel type ideals.

Abstract

An equigenerated monomial ideal $I$ in the polynomial ring $S= K[x_1,\ldots,x_n]$ is a Freiman ideal if $\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$ where $\ell(I)$ is the analytic spread of $I$ and $\mu(I)$ is the number of minimal generators of $I$. In this paper, we classify certain classes of Borel type ideals, including Borel ideals with multiple Borel generators and principal $k$-Borel ideals, which are Freiman.