Numerical semigroups: Ap,ry sets and Hilbert series

被引：18

作者：

Alfonsin, Jorge L. Ramirez ^{[1
]}

Rodseth, Oystein J. ^{[2
]}

机构：

[1] Univ Paris 06, Equipe Combinatoire & Optimisat, F-75252 Paris 05, France

[2] Univ Bergen, Dept Math, N-5008 Bergen, Norway

来源：

SEMIGROUP FORUM | 2009年 / 79卷 / 02期

关键词：

Numerical semigroup; Hilbert series; Apery set; Frobenius number; Genus; LINEAR DIOPHANTINE PROBLEM; ARITHMETIC SEQUENCES; FROBENIUS;

D O I：

10.1007/s00233-009-9133-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let a (1),aEuro broken vertical bar,a (n) be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a (1),aEuro broken vertical bar,a (n) . In this paper, we focus our attention on AA-semigroups, that is semigroups being generated by almost arithmetic progressions. After some general considerations, we give a characterization of the symmetric AA-semigroups. We also present an efficient method to determine an Ap,ry set and the Hilbert series of an AA-semigroup.

引用

页码：323 / 340

页数：18

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