Integer Partitions and Convexity
Faculty of Mathematics
Department of Operational Research
P. O. Box 32
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,
(Concerned with sequence
Received March 6 2007;
revised version received June 9 2007.
Published in Journal of Integer Sequences, June 10 2007.
Journal of Integer Sequences home page