[3] During the second half of the twentieth century, interest in the study of numerical semigroups resurfaced because of their applications in algebraic geometry.
The cardinality of the minimal set of generators is called the embedding dimension of the numerical semigroup S and is denoted by e(S).
The smallest member in the minimal system of generators is called the multiplicity of the numerical semigroup S and is denoted by m(S).
Numerical semigroups with small Frobenius number or genus The following general results were known to Sylvester.
Then There is no known general formula to compute the Frobenius number of numerical semigroups having embedding dimension three or more.
No polynomial formula can be found to compute the Frobenius number or genus of a numerical semigroup with embedding dimension three.
Such numerical semigroups have simple characterizations in terms of Frobenius number and genus: