A semilattice structure for the set of numerical semigroups with fixed Frobenius number

Details A semilattice structure for the set of numerical semigroups with fixed Frobenius number A semilattice structure for the set of numerical semigroups with fixed Frobenius number

2011-05-20

arxiv.org/abs/1105.4600v1

Mathematics

Commutative Algebra

11 pages

Scientific paper

We present a procedure to enumerate the whole set of numerical semigroups with a given Frobenius number F, S(F). The methodology is based on the construction of a partition of S(F) by a congruence relation. We identify exactly one irreducible and one homogeneous numerical semigroup at each class in the relation, and from those two elements we reconstruct the whole class. An alternative more efficient method is proposed based on the use of the Kunz-coordinates vectors of the elements in S(F).

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