2016
DOI: 10.48550/arxiv.1609.06515
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The Complexity of the Numerical Semigroup Gap Counting Problem

Abstract: In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined as a positive integer that does not belong to the numerical semigroup. The computation of gaps of numerical semigroups has been actively studied from the 19th century. However, little has been known on the computational complexity. In 2005, Ramírez-Alfonsín proposed a questi… Show more

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