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arXiv · 1705.04256

Characterizations of numerical semigroup complements via Apéry sets

T. Alden Gassert·Caleb McKinley Shor
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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 $m$.

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T. Alden Gassert, Caleb McKinley Shor. 2018-02-28. Characterizations of numerical semigroup complements via Apéry sets. https://arxiv.org/abs/1705.04256

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