Characterizations of Numerical Semigroup Complements Via Apéry Sets

Authors

T. Alden Gassert
Caleb Shor, Western New England UniversityFollow

College

College of Arts and Sciences

Department

Mathematics

Publication Date

3-19-2018

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 mth power Sylvester and alternating Sylvester sums for free numerical semigroups. Explicit formulas are given for small m.

Recommended Citation

Gassert, T. Alden and Shor, Caleb, "Characterizations of Numerical Semigroup Complements Via Apéry Sets" (2018). Faculty Publications - College of Arts and Sciences. 16.
https://digitalcommons.law.wne.edu/casfacpubs/16

Original Citation

Gassert, T.A., Shor, C.M. Characterizations of numerical semigroup complements via Apéry sets. Semigroup Forum 98, 31–47 (2019). https://doi.org/10.1007/s00233-018-9935-4