The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus

Abstract

We compute all possible numbers that are the Frobenius number of a numerical semigroup when multiplicity and genus are fixed. Moreover, we construct explicitly numerical semigroups in each case.

The set of numerical semigroups of a given multiplicity and Frobenius number

“…[13, Proposition 2.1]. If (m, g) ∈ N\{0}×N, then L (m, g) = ∅ if and only if (m, g) = (1, 0) or 2 ≤ m ≤ g + 1.…”