2000/09/18 by Krishnaswami Alladi, Alladi, Krishnaswami, Alexander Bérkovich +2
Mathematics · #05A19 #11P81 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A19 #msc:11P81 #msc:11P83
paper · pdf · doi:10.48550/arxiv.math/0009171
31 pages, 4 figures
arxiv created 2000/09/18 · openalex publication_date 2000/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts \not≡ 0, ± i (mod 6), and a set of three theorems involving partitions into parts \not≡ 0, ± i (mod 7), i=1,2,3.