RANK DIFFERENCES FOR OVERPARTITIONS
By Jeremy Lovejoy, Robert Osburn. 2007
55 citations recorded by the source corpus.
In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulae for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulae for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/1098ba12238f21ca08b117208f748af36bd4e0f7
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In Algebra and Number Theory
- Frank G. Garvan
- Robert Osburn
- Kathrin Bringmann
- Jeremy Lovejoy
- Chris Jennings-Shaffer
- Karl Mahlburg
- George E. Andrews
- Ken Ichi Ono
In Discrete Mathematics and Combinatorics
- Frank G. Garvan
- Kathrin Bringmann
- Robert Osburn
- Chris Jennings-Shaffer
- Jeremy Lovejoy
- Karl Mahlburg
- Robert C. Rhoades
- George E. Andrews
Citations in the corpus
- Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, result): “7) was one of the key results used to prove identities for rank differences for overpartitions in [27].”
- The spt-crank for overpartitions (2013, methodology): “1 of [24], although we’ve omitted their −1 term.”