Izvorni znanstveni članak
Some families of identities for the integer partition function
Ivica Martinjak
; Department of Physics, University of Zagreb, Zagreb, Croatia
Dragutin Svrtan
; Department of Mathematics, University of Zagreb, Zagreb, Croatia
Sažetak
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.
Ključne riječi
partition identity; partition function; Euler function; pentagonal numbers; Rogers-Ramanujan identities
Hrčak ID:
149784
URI
Datum izdavanja:
18.12.2015.
Posjeta: 1.235 *