Some families of identities for the integer partition function

Ivica Martinjak; Dragutin Svrtan

Vol. 20 No. 2 (2015)

Regular Articles

Some families of identities for the integer partition function

Published 2015-10-02

Ivica Martinjak
Dragutin Svrtan

Ivica Martinjak
University of Zagreb, Faculty of Science

Dragutin Svrtan

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Abstract

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

Keywords

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

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Author Biography

Ivica Martinjak

University of Zagreb

Faculty of Science

Assistant Professor