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

TL;DR

This paper precisely finds the maximum hook length in finitely many $d$-distinct $(s,t)$-core partitions and offers an algorithm to construct such partitions with this maximum hook length.

Contribution

It introduces an exact determination of the maximum hook length for $d$-distinct $(s,t)$-core partitions and provides a constructive algorithm.

Findings

Maximum hook length determined explicitly

Algorithm for constructing partitions with maximum hook length

Applicable to finitely many $d$-distinct $(s,t)$-core partitions

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.