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 / M. Barnabei; F. Bonetti; M.Silimbani. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 22:(2009), pp. 297-303. [10.1016/j.aml.2008.03.025]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.