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. 
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