2018/11/30 by Ali Kemal Uncu, Ali K. Uncu · 7 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics #Connection (principal bundle) #Discrete mathematics #Mathematics #Partition (number theory) #Ramanujan theta function #Ramanujan's sum #Representation (politics) #Series (stratigraphy) #math.CO #math.NT #msc:05A10 #msc:05A15 #msc:05A17 #msc:11B37 #msc:11B65 #msc:11C08 #msc:11P81 #msc:11P83 #msc:11P84
paper · pdf · doi:10.1016/j.disc.2021.112562
published in Discrete Mathematics 344(11), 112562 (Elsevier BV) · 24 pages
openalex publication_date 2021/07/26 · arxiv created 2021/07/27 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.