Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.3

Bounds for the Eventual Positivity of Difference Functions of Partitions

Roger Woodford
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.

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(Concerned with sequences A000607 and A090677 .)

Received April 10 2006; revised version received November 18 2006. Published in Journal of Integer Sequences December 29 2006.

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