Characterizations of numerical semigroup complements via Apéry sets

Abstract

In this paper, we generalize the work of Tuenter to give an identity which completely characterizes the complement of a numerical semigroup in terms of its Apéry sets. Using this result, we compute the $m$th power Sylvester and alternating Sylvester sums for free numerical semigroups. Explicit formulas are given for small $m$.

arXiv comment15 pages. Revisions submitted, February, 2018