Frobenius pseudo-variety of numerical semigroups with a given multiplicity and ratio

Abstract

AbstractIn this paper, we study the set $$\mathscr {L}(m,r)$$ L ( m , r ) of all numerical semigroups with multiplicity m and ratio r. In particular, we present some algorithms that compute all the elements of $$ \mathscr {L}(m,r)$$ L ( m , r ) with a given genus or with a given Frobenius number.