The right-generators descendant of a numerical semigroup

Bras-Amorós, Maria; Fernández-González, Julio

doi:10.1090/mcom/3502

The right-generators descendant of a numerical semigroup
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Math. Comp. 89 (2020), 2017-2030 Request permission

Abstract:

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.

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