Integer partitions with large Dyson rank
Number Theory
2023-03-20 v2 Combinatorics
Abstract
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 give formulas for the number of partitions of n with rank larger than n/2, and we prove identities for counts of partitions with large rank in fixed residue classes.
Cite
@article{arxiv.2203.08987,
title = {Integer partitions with large Dyson rank},
author = {Colin Alberts and Olivia Beckwith and Irfan Demetoglu and Robert Dicks and John H. Smith and Jasmine Wang},
journal= {arXiv preprint arXiv:2203.08987},
year = {2023}
}