Freiman $t$-spread principal Borel ideals

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