Asymptotics for rank partition functions

By Kathrin Bringmann. 2007

54 citations recorded by the source corpus.

In this paper, we obtain asymptotic formulas for an infinite class of rank generat- ing functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/191844eacddd1900110e90100249d874bd89c6eb

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

ON THE EXPLICIT CONSTRUCTION OF HIGHER DEFORMATIONS OF PARTITION STATISTICS (2007, methodology): “Viewing the rank generating functions in the framework of weak Maass forms has found many applications, including an exact formula for the coecients of f(q) [12], asymptotics for N(m;n) [ 8 ], and identities for rank dierences [14].”
Asymptotics for rank and crank moments (2009, background): “As a result, the study of generating functions from partition theory has inspired a number of important results about mock theta functions and harmonic Maass forms [9, 12, 14, 15].”
Inequalities between ranks and cranks (2009, methodology): “Remark. It should be possible to extend the inequalities from part (2) of Garvan’s conjecture to all n using known methods, although the estimates required are rather technical (see [ 8 ] for a related example and [11] for a more general setting).”
Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks (2007, result): “SC(q) in Theorem 15. 11. In light of Bringmann’s asymptotics for the rank partition functions [ 12 ], and the recent breakthroughs by Bringmann and Ono on the exact formulas for the coefficients in the power series of mock theta functions [13], provide similar results for Dk(n) and D 0 k (n).”
Partition Statistics and Quasiharmonic Maass Forms (2009, background): “These include, for example, an exact formula for the coecients of f(q) [9], asymptotics for N(m;n) [ 6 ], identities for rank dierences [11], and congruences for certain partition statistics [10].”