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A Sequence of Quasipolynomials Arising from Random Numerical Semigroups
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Calvin Leng

Department of Mathematics

University of California, Davis

Davis, CA 95616

USA

Christopher O'Neill

Department of Mathematics and Statistics

San Diego State University

San Diego, CA 92182

USA

**Abstract:**

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
*h*_{n,i}, that
count generating sets with certain properties. We prove a recurrence
that implies the sequence *h*_{n,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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