The number of smallest parts in the partitions of n

By George E. Andrews. 2008

197 citations recorded by the source corpus.

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Citations in the corpus

The spt-crank for overpartitions (2013, methodology): “We recall the spt function began with Andrews in [3] defining spt (n) as the number of smallest parts in the partitions of n.”
Rank and crank moments for overpartitions (2008, background): “When the overpartition has no overlined parts, spt(n) reduces to Andrews’ smallest parts function spt(n) [3, 16, 17].”
Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, methodology): “has an elegant combinatorial interpretation and satisfies some nice congruence properties [4].”
Asymptotic inequalities for positive crank and rank moments (2012, background): “In [3], Andrews defined the smallest parts function spt(N) as the sum of the total number of appearances of the smallest part in each integer partition of N , and proved the surprising fact that”
Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's Rank (2007, background): “In [ 3 ], Andrews found some surprising congruences for spt(n)”
Higher Order SPT-Functions (2010, background): “Introduction Andrews [3] defined the function spt(n) as the number of smallest parts in the partitions of n.”
Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q) (2015, background): “Now take the second derivative on both sides with respect to z, make use of the facts ([9] Equations (2.”
Asymptotics for rank and crank moments (2009, unknown): “Andrews proved [3] that spt(n) = np(n)− 1 2 N2(n).”