Bressoud-Subbarao type weighted partition identities for a generalized divisor function

2022/10/07 by Agarwal, Archit, Bhoria, Subhash Chand, Eyyunni, Pramod +1
#05A17 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11P84 #Secondary 11P81

paper · doi:10.48550/arxiv.2210.03457

Abstract

In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a q-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud-Subbarao type weighted partition identities beginning from an identity of Andrews, Garvan and Liang. We also found a one-variable generalization of an identity of Uchimura related to Bell polynomials.

Related

• Generalization of five q-series identities of Ramanujan and unexplored\n weighted partition identities
• A combinatorial proof of an identity for the divisor generating function
• Partition implications of a new three parameter q-series identity
• New Weighted Rogers-Ramanujan Partition Theorems and their Implications
• Overpartitions and Bressoud's conjecture, I