Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

By George E. Andrews. 2007

153 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/ae9a475efed2976859ef3dbcbe0409c595f2db9f

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's Rank (2007, unknown): “ollows. CONGRUENCES FOR THE SMALLEST PARTS FUNCTION AND THE RANK 23 7. Concludingremarks In a companion paper [14] we further explore the general problem of congruences mod ℓfor rank moments, Andrews [2] symmetrized rank moments and full rank functions for k-marked Durfee symbols for general ℓ. Let ”
ON THE EXPLICIT CONSTRUCTION OF HIGHER DEFORMATIONS OF PARTITION STATISTICS (2007, background): “We denote byD2(n) the number of 2-marked Durfee symbols arising from partitions of n. In [ 3 ] it is shown that”
Taylor coefficients of mock-Jacobi forms and moments of partition statistics (2014, background): “The symmetrized crank and rank moments studied by Garvan [22] and Andrews [1] are defined by”
Asymptotics for rank and crank moments (2009, background): “Additionally, Andrews introduced marked Durfee symbols in [3], which are combinatorial generalizations of partitions, and are intrinsically connected to crank and rank moments.”
Rank and crank moments for overpartitions (2008, background): “Since their introduction by Atkin and Garvan [4], the rank and crank moments and their linear combinations have been the subject of a number of works [ 2 , 3, 5, 6, 16, 17].”
Partition Statistics and Quasiharmonic Maass Forms (2009, methodology): “In [ 1 ] Andrews showed that k-marked Durfee symbols arise naturally in the combinatorial study of the rank moment functions; in particular, for k 1,”
Asymptotic inequalities for positive crank and rank moments (2012, unknown): “…was supported by NSF Grant DMS1201435. c©2013 American Mathematical Society Reverts to public domain 28 years from publication 1073 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use This was later followed by Garvan’s discovery of the…”
Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, methodology): “Proof. Since the proof is similar to the proof of [ 3, Theorem 2 ], we omit most of the details.”