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- Title
COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS.
- Authors
BLANCO, VÍCTOR; GARCÍA-SÁNCHEZ, PEDRO A.; PUERTO, JUSTO; Delgado, Manuel
- Abstract
This paper presents a new methodology to compute the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius number) and multiplicity. First, we give theoretical results about the polynomial-time complexity of counting these semigroups. We also illustrate the methodology analyzing the cases of multiplicity 3 and 4 where some formulas for the number of numerical semigroups for any genus and Frobenius number are obtained.
- Subjects
NUMERICAL analysis; SEMIGROUPS (Algebra); GENERATING functions; FROBENIUS algebras; NUMBER theory; POLYHEDRA; MULTIPLICITY (Mathematics)
- Publication
International Journal of Algebra & Computation, 2011, Vol 21, Issue 7, p1217
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196711006911