Dyson’s crank of a partition

1988/01/01 by George E. Andrews, Frank Garvan · 6 citations
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research

paper · pdf · doi:10.1090/s0273-0979-1988-15637-6

openalex publication_date 1988/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26

Abstract

largest part minus the number of parts. He let 7V(ra, t, n) denote the number of partitions of n of rank congruent to m modulo £, and he conjectured (1.1) 7V(m, 5,5n + 4) = ±p(5n + 4), 0 < m < 4; (1.2) JV(ra,7,7n + 5) = ±p(7n + 5), 0 < m < 6,

Cited by

• On the seventh order mock theta functions
• An interesting q-series related to the 4th symmetrized rank function
• Arithmetic properties of the partition function
• Distribution of the Partition Function Modulo m
• Counting the Ideals of Given Codimension of the Algebra of Laurent Polynomials in Two Variables
• Freeman Dyson [wikipedia]