GAP-Manual: 5.2 Constructing the set of all numerical semigroups containing a given numerical semigroup In order to construct the set of numerical semigroups containing a fixed numerical semigroup S, one first constructs its unitary extensions, that is to say, the sets S∪{g} that are numerical semigroups with g a positive integer. This is achieved by constructing the special gaps of the semigroup, and then adding each of them to the numerical semigroup. Then we repeat the process for each of this new numerical semigroups until we reach N.

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  1. Bras-Amorós, Maria; Fernández-González, Julio: The right-generators descendant of a numerical semigroup (2020)
  2. Eliahou, Shalom; Fromentin, Jean: Gapsets and numerical semigroups (2020)
  3. Eliahou, Shalom; Fromentin, Jean: Gapsets of small multiplicity (2020)
  4. Ojeda, I.; Rosales, J. C.: The arithmetic extensions of a numerical semigroup (2020)
  5. Song, Kyunghwan: The Frobenius problem for numerical semigroups generated by the Thabit numbers of the first, second kind base (b) and the Cunningham numbers (2020)
  6. Cisto, Carmelo; Failla, Gioia; Peterson, Chris; Utano, Rosanna: Irreducible generalized numerical semigroups and uniqueness of the Frobenius element (2019)
  7. Eliahou, Shalom; Fromentin, Jean: Near-misses in Wilf’s conjecture (2019)
  8. Leng, Calvin; O’Neill, Christopher: A sequence of quasipolynomials arising from random numerical semigroups (2019)
  9. Rosales, J. C.; Branco, M. B.: A problem of integer partitions and numerical semigroups (2019)
  10. Bras-Amorós, Maria; Fernández-González, Julio: Computation of numerical semigroups by means of seeds (2018)
  11. Castellanos, A. S.; Tizziotti, G.: On Weierstrass semigroup at (m) points on curves of the form (f(y)=g(x)) (2018)
  12. De Loera, Jesus; O’Neill, Christopher; Wilburne, Dane: Random numerical semigroups and a simplicial complex of irreducible semigroups (2018)
  13. Bernardini, Matheus; Torres, Fernando: Counting numerical semigroups by genus and even gaps (2017)
  14. Delgado, M.; García-Sánchez, P. A.: numericalsgps, a GAP package for numerical semigroups (2016)
  15. Failla, Gioia; Peterson, Chris; Utano, Rosanna: Algorithms and basic asymptotics for generalized numerical semigroups in (\mathbbN^d) (2016)
  16. Fromentin, Jean; Hivert, Florent: Exploring the tree of numerical semigroups. (2016)
  17. Gu, Ze; Tang, Xilin: The doubles of one half of a numerical semigroup. (2016)
  18. Ilhan, Sedat; Süer, Meral: On the saturated numerical semigroups (2016)
  19. Moyano-Fernández, Julio José; Uliczka, Jan: Duality and syzygies for semimodules over numerical semigroups (2016)
  20. Moyano-Fernández, Julio José; Uliczka, Jan: Lattice paths with given number of turns and semimodules over numerical semigroups (2014)

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