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Hook length biases for self-conjugate partitions and partitions with distinct odd parts

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Cossaboom,  Catherine
Max Planck Institute for Mathematics, Max Planck Society;

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2406.18480.pdf
(Preprint), 315KB

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Cossaboom, C. (submitted). Hook length biases for self-conjugate partitions and partitions with distinct odd parts.


Cite as: https://hdl.handle.net/21.11116/0000-000F-BD49-B
Abstract
We establish a hook length bias between self-conjugate partitions and partitions of distinct odd parts, demonstrating that there are more hooks of fixed length t≥2 among self-conjugate partitions of n than among partitions of distinct odd parts of n for sufficiently large n. More precisely, we derive asymptotic formulas for the total number of hooks of fixed length t in both classes. This resolves a conjecture of Ballantine, Burson, Craig, Folsom, and Wen.