Bounds for the Eventual Positivity of Difference Functions of Partitions
Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
In this paper we specialize work done by Bateman and Erdős
concerning difference functions of partition functions. In
particular, we are concerned with partitions into fixed powers of the
primes. We show that any difference function of these partition
functions is eventually increasing, and derive explicit bounds for
when it will attain strictly positive values. From these bounds an
asymptotic result is derived.
Full version: pdf,
(Concerned with sequences
Received April 10 2006;
revised version received November 18 2006.
Published in Journal of Integer Sequences, December 29 2006.
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