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