Almost symmetric numerical semigroups with given Frobenius number and type

Abstract

We give two algorithmic procedures to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number and type, and the whole set of almost symmetric numerical semigroups with fixed Frobenius number. Our algorithms allow to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number with similar or even higher efficiency that the known ones. They have been implemented in the GAP (http://www.gap-system.org) package NumericalSgps (http://www.gap-system.org/Packages/numericalsgps.html).

12 pages, 1 figure. References updated. A conjecture added (Remark 20). Accepted for publication in Journal of Algebra and its Applications