Some families of identities for the integer partition function
Martinjak, Ivica ; Svrtan, Dragutin
Mathematical Communications, Tome 20 (2015) no. 1, p. 193-200 / Harvested from Mathematical Communications
Text on Mathematical Communications
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
Publié le : 2015-11-08
Classification:  partition identity, partition function, Euler function, pentagonal numbers, Rogers-Ramanujan identities,  05A17; 11P84 
@article{mc1137,
     author = {Martinjak, Ivica and Svrtan, Dragutin},
     title = {Some families of identities for the integer partition function},
     journal = {Mathematical Communications},
     volume = {20},
     number = {1},
     year = {2015},
     pages = { 193-200},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc1137}
}

Martinjak, Ivica; Svrtan, Dragutin. Some families of identities for the integer partition function. Mathematical Communications, Tome 20 (2015) no. 1, pp.  193-200. http://gdmltest.u-ga.fr/item/mc1137/