Freiman Borel type ideals

Abstract

An equigenerated monomial ideal $I$ in the polynomial ring $S=K[x_1,\dots ,x_n]$ 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 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.

16 pages, 3 figure