Numerical Semigroups of Sally Type II

Abstract

In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $\hat{I}½\ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We also construct a minimal resolution for another special class of such semigroups of type $\hat{I}½-1$. Finally, we propose some conjectures for the Betti numbers of families of non-symmetric Sally type semigroups in the above cases in relation to those of the corresponding Gorenstein cases of Sally type semigroups.

21 pages