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Some Families of Identities for the Integer Partition Function (CROSBI ID 221408)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Martinjak, Ivica ; Svrtan, Dragutin Some Families of Identities for the Integer Partition Function // Mathematical communications, 20 (2015), 2; 193-200

Podaci o odgovornosti

Martinjak, Ivica ; Svrtan, Dragutin

engleski

Some Families of Identities for the Integer Partition Function

We give series of recursive identities for the number of partitions with exactly $k$ parts and with constraints on both the minimal difference among the parts and the minimal part. Using these results we demonstrate that the number of partitions of $n$ is equal to the number of partitions of $2n+d{; ; ; ; n \choose 2}; ; ; ; $ of length $n$, with $d$-distant parts. We also provide a direct proof for this identity. This work is the result of our aim at finding a bijective proof for Rogers-Ramanujan identities.

partition identity ; partition function ; Euler function ; pentagonal numbers ; Rogers-Ramanujan identities

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Podaci o izdanju

20 (2)

2015.

193-200

objavljeno

1331-0623

1848-8013

Povezanost rada

Matematika

Indeksiranost