Integer Partitions and Convexity
Sadek Bouroubi
USTHB
Faculty of Mathematics
Department of Operational Research
Laboratory LAID3
P. O. Box 32
16111 El-Alia
Bab-Ezzouar, Algiers
Algeria
Abstract:
Let n be an integer >=1, and let p(n,k) and
P(n,k) count the number of partitions
of n into k parts, and the number of partitions of n
into parts less than or equal to k, respectively.
In this paper, we show that these
functions are convex. The result includes the actual value of the
constant of Bateman and Erdős.
Full version: pdf,
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latex
(Concerned with sequence
A026812.)
Received March 6 2007;
revised version received June 9 2007.
Published in Journal of Integer Sequences, June 10 2007.
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