  For the elements of a numerical semigroup which are larger than the Frobenius
number, we introduce the definition of, seed, by broadening the notion of
generator. This new concept allows us to explore the semigroup tree in an
alternative efficient way, since the seeds of each descendant can be easily
obtained from the seeds of its parent. The paper is devoted to presenting the
results which are related to this approach, leading to a new algorithm for
computing and counting the semigroups of a given genus.

Combinatorics