Freiman $t$-spread principal Borel ideals

Abstract

An equigenerated monomial ideal $I$ is a Freiman ideal if $\mu (I^2)=\ell (I)\mu (I)-\left(\genfrac{}{}{0ex}{}{\ell (I)}{2}\right)$ 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.