A Sequence of Quasipolynomials Arising from Random Numerical Semigroups
Department of Mathematics
University of California, Davis
Davis, CA 95616
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
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.
Full version: pdf,
(Concerned with sequences
Received October 9 2018; revised version received August 7 2019.
Published in Journal of Integer Sequences,
August 24 2019.
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