@**article**{RISC5800,author = {Ali Kemal Uncu},

title = {{On double sum generating functions in connection with some classical partition theorems }},

language = {english},

abstract = { 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. },

journal = {ArXiv e-prints},

pages = {1--20},

isbn_issn = {N/A},

year = {2018},

refereed = {yes},

length = {20}

}