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.