# On Symmetric But Not Cyclotomic Numerical Semigroups

@article{Sawhney2017OnSB, title={On Symmetric But Not Cyclotomic Numerical Semigroups}, author={Mehtaab Sawhney and David Stoner}, journal={SIAM J. Discret. Math.}, year={2017}, volume={32}, pages={1296-1304} }

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…

## 5 Citations

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A numerical semigroup S is cyclotomic if its semigroup polynomial PS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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