School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
4-20-2023
Abstract
For 80 years, Dyson’s rank has been known as the partition statistic that witnesses the first two of Ramanujan’s celebrated congruences for the ordinary partition function. In this paper, we show that Dyson’s rank actually witnesses families of partition congruences modulo every prime . This comes from an in-depth study of when a “multiplicity-based statistic” is a crank witnessing congruences for the function p ` n, m˘ , which enumerates partitions of n with parts of size at most m. We also show that as the modulus increases, there is an ever-growing collection of distinct multiplicity-based cranks witnessing these same families.
Recommended Citation
Eichhorn, Dennis, Brandt Kronholm, and Acadia Larsen. "Cranks for partitions with bounded largest part." Proceedings of the American Mathematical Society 151, no. 08 (2023): 3291-3303. https://doi.org/10.1090/proc/16399
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Proc. Amer. Math. Soc
DOI
https://doi.org/10.1090/proc/16399
Comments
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