Journal of the Ramanujan Mathematical Society
Volume 38, Issue 1, March 2023 pp. 15–21.
Integer partitions with large Dyson rank
Authors:
Colin Albert, Olivia Beckwith, Irfan Demetoglu, Robert Dicks, John H. Smith and Jasmine Wang
Author institution:
University of Illinois at Urbana-Champaign, IL 61820, United States.
Summary:
The Dyson rank of an integer partition is the difference between its largest part and the number of parts it contains. Using Fine-Dyson symmetry, we study counts of partitions whose rank lies in fixed residue classes and has large absolute value. We prove formulas relating these counts for partitions of different sizes.
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