The maximum hook length of $d$-distinct simultaneous core partitions

Benjamin Przybocki; Ethan Pesikoff; Janabel Xia

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The maximum hook length of $d$-distinct simultaneous core partitions

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arxiv 2209.09973 v1 pith:EW5ZLR4K submitted 2022-09-20 math.CO math.NT

Ethan Pesikoff , Benjamin Przybocki , Janabel Xia This is my paper · ORCID

classification math.COmath.NT

keywords coredistincthooklengthmaximumpartitionspossiblealgorithm

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abstract

We exactly determine the maximum possible hook length of $(s,t)$-core partitions with $d$-distinct parts when there are finitely many such partitions. Moreover, we provide an algorithm to construct a $d$-distinct $(s,t)$-core partition with this maximum possible hook length.

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