Ali Kemal Uncu,
"On double sum generating functions in connection with some classical partition theorems"
, in ArXiv e-prints, Seite(n) 1--20, 2018
On double sum generating functions in connection with some classical partition theorems
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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, Göllnitz--Gordon, and little Göllnitz 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.
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