On the generators of a generalized numerical semigroup

Abstract

We give a characterization on the sets A ⊆ ℕd such that the monoid generated by A is a generalized numerical semigroup (GNS) in ℕd. Furthermore we give a procedure to compute the hole set ℕd \ S, where S is a GNS, if a finite set of generators of S is known.

Keywords

• generalized numerical semigroup
• minimal generators
• primary 20m14, 05a15
• secondary 05a16, 11d07