# Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers

@article{Moree2014NumericalSC,
title={Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers},
author={Pieter Moree},
journal={The American Mathematical Monthly},
year={2014},
volume={121},
pages={890 - 902}
}
• P. Moree
• Published 19 August 2013
• Mathematics
• The American Mathematical Monthly
Abstract We give two proofs of a folklore result relating numerical semigroups of embedding dimension two and binary cyclotomic polynomials and explore some consequences. In particular, we give a more conceptual reproof of a result of Hong et al. (2012) on gaps between the exponents of nonzero monomials in a binary cyclotomic polynomial. The intent of this paper is to better unify the various results within the cyclotomic polynomial and numerical semigroup communities.
31 Citations
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