Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.2

A Sequence of Quasipolynomials Arising from Random Numerical Semigroups

Calvin Leng
Department of Mathematics
University of California, Davis
Davis, CA 95616

Christopher O'Neill
Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182


A numerical semigroup is a cofinite subset of the non-negative integers that is closed under addition. For a randomly generated numerical semigroup, the expected number of minimum generators can be expressed in terms of a doubly-indexed sequence of integers, denoted hn,i, that count generating sets with certain properties. We prove a recurrence that implies the sequence hn,i is eventually quasipolynomial when the second parameter is fixed.

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(Concerned with sequences A158206 A319608.)

Received October 9 2018; revised version received August 7 2019. Published in Journal of Integer Sequences, August 24 2019.

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