On the Type and the Minimal Presentation of Certain Numerical Semigroups

Abstract

We study numerical semigroups generated by generalized arithmetic sequences. We present a membership criterion for such a numerical semigroup, and by this we are able to answer fundamental questions concerning a numerical semigroup such as computing the Frobenius number and the type of the numerical semigroup, and decide whether the numercial semigroup is symmetric. Also for this kind of numerical semigroups, we compute the cardinality of a minimal presentation and determine whether they are complete intersections.

Key Words:

• Frobenius number
• Minimal presentation
• Numerical semigroup
• Type

2000 Mathematics Subject Classification:

• 13D45
• 16W50
• 14B15

Notes

Communicated by I. Swanson.