Computing the number of numerical semigroups using generating functions

Details Computing the number of numerical semigroups using generating functions Computing the number of numerical semigroups using generating functions

2009-01-09

arxiv.org/abs/0901.1228v3

Mathematics

Combinatorics

14 pages, 1 figure

Scientific paper

This paper presents a new methodology to count 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 the number of 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.

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