137 research outputs found
On double sum generating functions in connection with some classical partition theorems
We focus on writing closed forms of generating functions for the number of
partitions with gap conditions as double sums starting from a combinatorial
construction. Some examples of the sets of partitions with gap conditions to be
discussed here are the set of Rogers--Ramanujan, G\"ollnitz--Gordon, and little
G\"ollnitz partitions. This work also includes finding the finite analogs of
the related generating functions and the discussion of some related series and
polynomial identities. Additionally, we present a different construction and a
double sum representation for the products similar to the ones that appear in
the Rogers--Ramanujan identities.Comment: 20 page
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