Characterizations of numerical semigroup complements via Ap\'ery sets
Number Theory
2018-03-01 v2
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 Ap\'ery sets. Using this result, we compute the th power Sylvester and alternating Sylvester sums for free numerical semigroups. Explicit formulas are given for small .
Keywords
Cite
@article{arxiv.1705.04256,
title = {Characterizations of numerical semigroup complements via Ap\'ery sets},
author = {T. Alden Gassert and Caleb McKinley Shor},
journal= {arXiv preprint arXiv:1705.04256},
year = {2018}
}
Comments
15 pages. Revisions submitted, February, 2018