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
Cyclotomic numerical semigroup polynomials with few irreducible factors
- 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)…
Coefficients and higher order derivatives of cyclotomic polynomials: Old and new
- MathematicsExpositiones Mathematicae
- 2020
Cyclotomic numerical semigroup polynomials with at most two irreducible factors
- MathematicsSemigroup 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
Cyclotomic Numerical Semigroups
- MathematicsSIAM 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.
Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers
- MathematicsAm. Math. Mon.
- 2014
The intent of this paper is to better unify the various results within the cyclotomic polynomial and numerical semigroup communities.
Monic Polynomials in Z[x] with Roots in the Unit Disc
- MathematicsAm. Math. Mon.
- 2001
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.
The Complex Zeros of Random Polynomials
- 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…
numericalsgps, a GAP package for numerical semigroups
- MathematicsACCA
- 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