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.
Keywords:Freiman ideal, sorted ideal,
$t$-spread principal Borel ideal, sorted graph.