Numerical semigroups: Apéry sets and Hilbert series

Let a 1 ,…, a n be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a 1 ,…, a n . In this paper, we focus our attention on AA-semigroups, that is semigroups being generated by almost arithmetic progressions. After some gener...

Full description

Saved in:
Bibliographic Details
Published inSemigroup forum Vol. 79; no. 2; pp. 323 - 340
Main Authors Ramírez Alfonsín, Jorge L., Rødseth, Øystein J.
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.09.2009
Subjects
Algebra
Mathematics
Mathematics and Statistics
Research Article
Numerical semigroup
Apéry set
Frobenius number
Hilbert series
Genus
Online AccessGet full text

Cover

More Information
Summary:Let a 1 ,…, a n be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a 1 ,…, 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 Apéry set and the Hilbert series of an AA-semigroup.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-009-9133-5