The right-generators descendant of a numerical semigroup
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For a numerical semigroup, we encode the set of primitive elements that are larger than its Frobenius number and show how to produce in a fast way the corresponding sets for its children in the semigroup tree. This allows us to present an efficient algorithm for exploring the tree up to a given genus. The algorithm exploits the second nonzero element of a numerical semigroup and the particular pseudo-ordinary case in which this element is the conductor
CitationBras, M.; Fernández, J. The right-generators descendant of a numerical semigroup. "Mathematics of computation", 1 Gener 2020, vol. 89, núm. 324, p. 2017-2030.