Some Families of Identities for Integer Partition Function

2014/01/28 by Martinjak, Ivica, Svrtan, Dragutin
#05A17 #11P84 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.7123

Abstract

We give a 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+dn \choose 2 with n 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.

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