On Symmetric But Not Cyclotomic Numerical Semigroups

  title={On Symmetric But Not Cyclotomic Numerical Semigroups},
  author={Mehtaab Sawhney and David Stoner},
  journal={SIAM J. Discret. Math.},
A numerical semigroup is called cyclotomic if its corresponding numerical semigroup polynomial $P_S(x)=(1-x)\sum_{s\in S}x^s$ is expressable as the product of cyclotomic polynomials. Ciolan, Garcia-Sanchez, and Moree conjectured that for every embedding dimension at least $4$, there exists some numerical semigroup which is symmetric but not cyclotomic. We affirm this conjecture by giving an infinite class of numerical semigroup families $S_{n, t}$, which for every fixed $t$ is symmetric but not… 

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  • Numerical semigroups,
  • 2009

Higher order derivatives of the cyclotomic polynomial evaluated at˘1