2011/02/09 by Kathrin Bringmann, Ben Kane, Bringmann, Kathrin +1
Mathematics · #05A19 #05A20 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1102.1814
openalex publication_date 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dyson's rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequality, we show that such non-trivial identities are also rare for the full rank, but on the other hand we obtain an infinite family of non-trivial identities, contrasting the partition theoretic case.