Rank and crank moments for overpartitions
By Kathrin Bringmann, Jeremy Lovejoy, Robert Osburn. 2008
110 citations recorded by the source corpus.
We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H(n).
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/5237851d2be32bcf7586ca46f8646ea97292579d
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In Algebra and Number Theory
- Robert Osburn
- Kathrin Bringmann
- Jeremy Lovejoy
- George E. Andrews
- Frank G. Garvan
- Karl Mahlburg
- Ken Ichi Ono
- V. Spiridonov
In Discrete Mathematics and Combinatorics
- Kathrin Bringmann
- Robert Osburn
- Jeremy Lovejoy
- George E. Andrews
- Frank G. Garvan
- Karl Mahlburg
- V. Spiridonov
- Ken Ichi Ono
Citations in the corpus
- Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, background): “These partial differential equations are of independent interest [5], [12], [15].”
- RANK DIFFERENCES FOR OVERPARTITIONS (2007, background): “For more on these three ranks and their generating functions, see [4, 5, 7, 8, 9, 11, 13, 19, 20, 22, 23].”
- Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q) (2015, background): “For generalizations and analogues of spt(n), we refer the reader to [12, 18, 20, 23, 27, 28].”