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Integer partitions with large Dyson rank
Published 16 Mar 2022 in math.NT and math.CO | (2203.08987v2)
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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