On partition functions of Andrews and Stanley

摘要

Andrews has established a refinement of the generating function for partitions pi according to the numbers r(pi) and s(pi) of odd parts in pi and the conjugate of pi, respectively. In this paper, we derive a refined generating function for partitions into at most M parts less than or equal to N, which is a finite case of Andrew's refinement. (C) 2004 Elsevier Inc. All rights reserved.