CYCLOTOMIC NUMERICAL SEMIGROUPS

被引：12

作者：

Ciolan, Emil-Alexandru ^{[1
]}

Garcia-Sanchez, Pedro A. ^{[2
,3
]}

Moree, Pieter ^{[4
]}

机构：

[1] Univ Bonn, Regina Pacis Weg 3, D-53113 Bonn, Germany

[2] Univ Granada, IEMath GR, E-18071 Granada, Spain

[3] Univ Granada, Dept Algebra, E-18071 Granada, Spain

[4] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2016年 / 30卷 / 02期

关键词：

numerical semigroups; cyclotomic polynomials; semigroup polynomials; cyclotomic numerical semigroups; cyclotomic exponents; polynomially related semigroups; MAXIMAL HEIGHT; DIVISORS; POLYNOMIALS; CODES;

D O I：

10.1137/140989479

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a numerical semigroup S, we let P-S(x) - (1 - x) Sigma(s is an element of S) x(s) be its semigroup polynomial. We study cyclotomic numerical semigroups; these are numerical semigroups S such that P-S(x) has all its roots in the unit disc. We conjecture that S is a cyclotomic numerical semigroup if and only if S is a complete intersection numerical semigroup and present some evidence for it. Aside from the notion of cyclotomic numerical semigroups we introduce the notion of cyclotomic exponents and polynomially related numerical semigroups. We derive some properties and give some applications of these new concepts.

引用

页码：650 / 668

页数：19

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