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EnglishLet 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.
| Titolo: | Bijections and recurrences for integer partitions in a bounded number of parts | |
| Autore/i: | BARNABEI, MARILENA; BONETTI, FLAVIO; SILIMBANI, MATTEO | |
| Autore/i Unibo: | ||
| Anno: | 2009 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aml.2008.03.025 | |
| 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. | |
| Data prodotto definitivo in UGOV: | 2009-02-09 10:17:09 | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/62766
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