Let Πs(n) denote the set of partitions of the integer n into exactly s parts, and image the subset of Πs(n) containing all partitions whose two largest parts coincide. We present a bijection between image and Πs−1(m) for a suitable m<n in the cases s=3,4. Such bijections yield recurrence formulas for the numbers P3(n) and P4(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.

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

BARNABEI, MARILENA;BONETTI, FLAVIO;SILIMBANI, MATTEO
2009

Abstract

Let Πs(n) denote the set of partitions of the integer n into exactly s parts, and image the subset of Πs(n) containing all partitions whose two largest parts coincide. We present a bijection between image and Πs−1(m) for a suitable m<n in the cases s=3,4. Such bijections yield recurrence formulas for the numbers P3(n) and P4(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.
M. Barnabei; F. Bonetti; M.Silimbani
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/62766
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