Acute Semigroups, the Order Bound on the Minimum Distance, and the Feng–Rao Improvements

Abstract

We introduce a new class of numerical semigroups, which we call the class of acute semigroups and we prove that they generalize symmetric and pseudosymmetric numerical semigroups, Arf numerical semigroups, and the semigroups generated by an interval. For a numerical semigroup /spl Lambda/={/spl lambda//sub 0/ i})=/spl nu//sub i+1/ for all i/spl ges/m. We prove that the only numerical semigroups for which the sequence (/spl nu//sub i/) is always nondecreasing are ordinary numerical semigroups. Furthermore, we show that a semigroup can be uniquely determined by its sequence (/spl nu//sub i/).