Exploring the tree of numerical semigroups In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well-suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing very large optimizations: we obtain the number of numerical semigroups of genus $gleq 67$ and we confirm the Wilf conjecture for $gleq 60$.

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  1. Branco, Manuel B.; Ojeda, Ignacio; Rosales, José Carlos: The set of numerical semigroups of a given multiplicity and Frobenius number (2021)
  2. Eliahou, Shalom; Marín-Aragón, Daniel: On numerical semigroups with at most 12 left elements (2021)
  3. Spirito, Dario: Wilf’s conjecture for numerical semigroups with large second generator (2021)
  4. Bernardini, Matheus: Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors (2020)
  5. Bras-Amorós, Maria; Fernández-González, Julio: The right-generators descendant of a numerical semigroup (2020)
  6. Bruns, Winfried; García-Sánchez, Pedro; O’Neill, Christopher; Wilburne, Dane: Wilf’s conjecture in fixed multiplicity (2020)
  7. Delgado, Manuel: Conjecture of Wilf: a survey (2020)
  8. Díaz-Ramírez, J. D.; García-García, J. I.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A.: A geometrical characterization of proportionally modular affine semigroups (2020)
  9. Eliahou, Shalom: A graph-theoretic approach to Wilf’s conjecture (2020)
  10. Eliahou, Shalom; Fromentin, Jean: Gapsets and numerical semigroups (2020)
  11. Eliahou, Shalom; Fromentin, Jean: Gapsets of small multiplicity (2020)
  12. Maugeri, Nicola; Zito, Giuseppe: The tree of good semigroups in (\mathbbN^2) and a generalization of the Wilf conjecture (2020)
  13. Alhajjar, Elie; Russell, Travis; Steward, Michael: Numerical semigroups and Kunz polytopes (2019)
  14. Barucci, V.; Strazzanti, F.: Dilatations of numerical semigroups (2019)
  15. Eliahou, Shalom; Fromentin, Jean: Near-misses in Wilf’s conjecture (2019)
  16. García-García, Juan Ignacio; Marín-Aragón, Daniel; Moreno-Frías, María Ángeles; Rosales, José Carlos; Vigneron-Tenorio, Alberto: Semigroups with fixed multiplicity and embedding dimension (2019)
  17. Bras-Amorós, Maria; Fernández-González, Julio: Computation of numerical semigroups by means of seeds (2018)
  18. Delgado, Manuel: On a question of Eliahou and a conjecture of Wilf (2018)
  19. Bernardini, Matheus; Torres, Fernando: Counting numerical semigroups by genus and even gaps (2017)
  20. Kaplan, Nathan: Counting numerical semigroups (2017)

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