Integer partitions with large Dyson rank

Colin Alberts; Olivia Beckwith; Irfan Demetoglu; Robert Dicks; John H. Smith; Jasmine Wang

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arXiv · 2203.08987

Integer partitions with large Dyson rank

Colin Alberts·Olivia Beckwith·Irfan Demetoglu·Robert Dicks·John H. Smith·Jasmine Wang

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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.

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Colin Alberts, Olivia Beckwith, Irfan Demetoglu, Robert Dicks, John H. Smith, Jasmine Wang. 2022-03-16. Integer partitions with large Dyson rank. https://arxiv.org/abs/2203.08987

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