Relations between the ranks and cranks of partitions

2002/08/06 by A. O. L. Atkin, Atkin, A. O. L., F. G. Garvan +1 · 2 citations
Mathematics · #05A19 #11F11 #11F25 #11F33 (Secondary) #11P81 #11P83 (Primary) 05A17 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A17 #msc:05A19 #msc:11F11 #msc:11F25 #msc:11F33 #msc:11P81 #msc:11P83

paper · pdf · doi:10.48550/arxiv.math/0208050

24 pages

arxiv created 2002/08/06 · arxiv updated 2009/11/30

Abstract

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

Cited by

• On an spt function for the 4-th symmetrized crank function
• Mock modular forms from the k-rank moments

Related

• Andrews-Beck Type Congruences Related to the Crank of a Partition
• Rank partition functions and truncated theta identities
• Cranks for Ramanujan-type congruences of k-colored partitions
• Rank and Crank Moments for Partitions without Repeated Odd Parts
• Partitions weighted by the parity of the crank