On the Frobenius Problem of Numerical Semigroups

Abstract

We define the minimal transversal of a numerical semigroup with respect to one of its elements and use it to calculate the Frobenius number, genus, and the Hilbert function of the semigroup. We give various examples for the use of this method.

Key Words:

• The diophantine Frobenius problem
• Frobenius number
• Genus
• Hilbert function
• Numerical semigroups

2000 Mathematics Subject Classification:

• 11D45

Notes

Communicated by A. K. Singh.