The Ranks and Cranks of Partitions Moduli 2, 3, and 4

By G. Andrews, Richard P. Lewis. 2000

67 citations recorded by the source corpus.

Abstract We discuss inequalities between the rank counts N ( r ,  m ,  n ) and between the crank counts M ( r ,  m ,  n ), for m =2, 3, and 4, and state three conjectures.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/41371cd057577d529492b2444d75d53b2ae4ca1a

Citations in the corpus

• Asymptotics for rank partition functions (2007, unknown): “ π 6k √ 24n −1 + 8 √ 3sin πj c √ 24n −1 X k,r c∤k δc,k,r>0 Dj,c,k(−n,mj,c,k,r) √ k sinh r 2δc,k,r(24n −1) 3 π k !! +Oc (nǫ). This corollary implies some conjectures of Andrews and Lewis. In [4, 13] they showed N(0,2;2n) < N(1,2;2n) if n ≥ 1, N(0,4;n) > N(2,4;n) if 26 < n ≡ 0,1 (mod 4)”