Freiman $t$-spread principal Borel ideals

TL;DR

This paper classifies Freiman t-spread principal Borel ideals, a special class of monomial ideals with predictable generator counts for their powers, based on their algebraic properties.

Contribution

It provides a complete classification of Freiman t-spread principal Borel ideals, expanding understanding of their structure and properties.

Findings

Complete classification of Freiman t-spread principal Borel ideals

Explicit formulas for the number of generators of their powers

Identification of conditions characterizing these ideals

Abstract

An equigenerated monomial ideal $I$ 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 least number of monomial generators of $I$. Freiman ideals are special since there exists an exact formula computing the least number of monomial generators of any of their powers. In this paper we give a complete classification of Freiman $t$-spread principal Borel ideals.