# 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}
}
• Published 3 July 2017
• Mathematics
• 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…
• Mathematics
• 2021
A numerical semigroup S is cyclotomic if its semigroup polynomial PS is a product of cyclotomic polynomials. The number of irreducible factors of PS (with multiplicity) is the polynomial length l(S)
• Mathematics
Semigroup Forum
• 2021
A numerical semigroup S is cyclotomic if its semigroup polynomial PS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}

## References

SHOWING 1-8 OF 8 REFERENCES

• Mathematics
SIAM J. Discret. Math.
• 2016
The notion of cyclotomic exponents and polynomially related numerical semigroups is introduced and some properties are derived and some applications of these new concepts are given.
The intent of this paper is to better unify the various results within the cyclotomic polynomial and numerical semigroup communities.
This note is motivated by an old result of Kronecker on monic polynomials with integer coefficients having all their roots in the unit disc, and describes a canonical form for such polynmials and uses it to determine the sequence of k(n) for small values of n.
• Mathematics
• 1995
Mark Kac gave an explicit formula for the expectation of the number, vn (a), of zeros of a random polynomial, n-I Pn(z) = E ?tj, j=O in any measurablc subset Q of the reals. Here, ... ?In-I are
• Mathematics
ACCA
• 2016
The package numericalsgps performs computations with and for numerical and affine semigroups. This manuscript is a survey of what the package does, and at the same time intends to gather the trending

### A Garćıa-Sánchez

• Numerical semigroups,
• 2009