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.

References in zbMATH (referenced in 28 articles )

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  1. Failla, Gioia; Peterson, Chris; Utano, Rosanna: Algorithms and basic asymptotics for generalized numerical semigroups in $\mathbb N^d$ (2016)
  2. Fromentin, Jean; Hivert, Florent: Exploring the tree of numerical semigroups. (2016)
  3. Gu, Ze; Tang, Xilin: The doubles of one half of a numerical semigroup. (2016)
  4. Moyano-Fernández, Julio José; Uliczka, Jan: Lattice paths with given number of turns and semimodules over numerical semigroups (2014)
  5. Assi, A.; García-Sánchez, P.A.: Constructing the set of complete intersection numerical semigroups with a given Frobenius number. (2013)
  6. Nari, Hirokatsu: Symmetries on almost symmetric numerical semigroups. (2013)
  7. Blanco, Víctor; Puerto, Justo: An application of integer programming to the decomposition of numerical semigroups (2012)
  8. Blanco, Víctor; Rosales, José Carlos: On the enumeration of the set of numerical semigroups with fixed Frobenius number. (2012)
  9. Blanco, V.; Rosales, J.C.: The set of numerical semigroups of a given genus. (2012)
  10. Bras-Amorós, Maria: The ordinarization transform of a numerical semigroup and semigroups with a large number of intervals. (2012)
  11. Kaplan, Nathan: Counting numerical semigroups by genus and some cases of a question of Wilf. (2012)
  12. Blanco, Víctor; García-Sánchez, Pedro A.; Puerto, Justo: Counting numerical semigroups with short generating functions. (2011)
  13. Blanco, V.; Rosales, J.C.: Irreducibility in the set of numerical semigroups with fixed multiplicity. (2011)
  14. Rosales, J.C.; Branco, M.B.: The Frobenius problem for numerical semigroups (2011)
  15. Elizalde, Sergi: Improved bounds on the number of numerical semigroups of a given genus (2010)
  16. Bras-Amorós, Maria: Bounds on the number of numerical semigroups of a given genus (2009)
  17. Bras-Amorós, Maria; Bulygin, Stanislav: Towards a better understanding of the semigroup tree (2009)
  18. Rosales, J.C.: Atoms of the set of numerical semigroups with fixed Frobenius number. (2009)
  19. Delgado, M.; García-Sánchez, P.A.; Rosales, J.C.; Urbano-Blanco, J.M.: Systems of proportionally modular Diophantine inequalities. (2008)
  20. Bras-Amorós, Maria; de Mier, Anna: Representation of numerical semigroups by Dyck paths. (2007)

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