Cyclotomic Numerical Semigroups

DOI10.1137/140989479zbMath1343.20060arXiv1409.5614OpenAlexW2246789780MaRDI QIDQ2800181

Emil-Alexandru Ciolan, Pieter Moree, Pedro A. García Sánchez

Publication date: 15 April 2016

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5614

zbMATH Keywords

cyclotomic polynomialsnumerical semigroupscomplete intersection semigroups

Mathematics Subject Classification ID

Commutative semigroups (20M14) Polynomials in number theory (11C08) Special sequences and polynomials (11B83) The Frobenius problem (11D07)

Related Items

Cyclotomic exponent sequences of numerical semigroups ⋮ On Symmetric But Not Cyclotomic Numerical Semigroups ⋮ Cyclotomic numerical semigroup polynomials with at most two irreducible factors ⋮ Newman cyclotomic polynomials, refinable splines and the Euler binary partition function ⋮ Isolated factorizations and their applications in simplicial affine semigroups ⋮ Characterizations of numerical semigroup complements via Apéry sets ⋮ Coefficients and higher order derivatives of cyclotomic polynomials: old and new (with an appendix by Pedro García-Sánchez) ⋮ On partitions and Arf semigroups ⋮ Commutative algebra and the linear diophantine problem of Frobenius ⋮ Augmented Hilbert series of numerical semigroups ⋮ Square-free divisor complexes of certain numerical semigroup elements ⋮ Cyclotomic coefficients: gaps and jumps ⋮ Graded algebras with cyclotomic Hilbert series ⋮ Algebraic stories from one and from the other pockets

Uses Software

• numericalsgps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On binary cyclotomic polynomials
• On free resolutions of some semigroup rings
• Some conjectures on the maximal height of divisors of \(x^n - 1\)
• Sparse binary cyclotomic polynomials
• Numerical semigroups: Apéry sets and Hilbert series.
• Bounds for the maximal height of divisors of \(x^n - 1\)
• Frobenius vectors, Hilbert series and gluings of affine semigroups.
• Numerical semigroups.
• Semi-groupes d'entiers et application aux branches
• Approximation of singular series and automata
• Maximal height of divisors of \(x^n-1\)
• Huneke-Wiegand conjecture for complete intersection numerical semigroup rings.
• Generators and relations of abelian semigroups and semigroup rings
• Monic Polynomials in Z[x with Roots in the Unit Disc]
• Several Proofs of the Irreducibility of the Cyclotomic Polynomials
• Maximal height of divisors of x^pqb – 1
• Sous-monoïdes d'intersection complète de $N$
• On the Middle Coefficient of a Cyclotomic Polynomial
• The minimum distance of codes in an array coming from telescopic semigroups
• Coefficient convexity of divisors of xn - 1
• Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers
• numericalsgps, a GAP package for numerical semigroups
• On the Weight Hierarchy of Codes Coming From Semigroups With Two Generators