Bijections and recurrences for integer partitions into a bounded number of parts

摘要

Let Pi(s)(n) denote the set of partitions of the integer n into exactly s parts, and 17,121 (n) the subset of Pi(s)(n) containing all partitions whose two largest parts coincide. We present a bijection between Pi((2))(s)(n) and Pi(s-1) (m) for a suitable m < n in the cases s = 3, 4. Such bijections yield recurrence formulas for the numbers P-3(n) and P-4(n) of partitions of n into 3 and 4 parts. Furthermore, we show that the present approach can be extended to the case s = 5, 6. (C) 2008 Elsevier Ltd. All rights reserved