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arXiv · 2610.35322

Maximum length and size of simultaneous core partitions with distinct parts

Metin Can Aydemir
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Abstract

We give, for the first time, a formula for the largest size of an $(s,t)$-core partition with distinct parts valid for every coprime pair. We also determine the greatest number of parts of an $(s,t)$-core partition whose successive parts differ by at least $D$, whenever $\gcd(s,t)\le D$, removing the restrictions on the core parameters in the formula of Burson, Sisneros-Thiry, and Straub. The size formula uses a column description and a single Dedekind sum. The length formula uses coefficients from the Euclidean algorithm and satisfies a recurrence in smaller core parameters. We construct partitions attaining each maximum.

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Metin Can Aydemir. 2026-10-26. Maximum length and size of simultaneous core partitions with distinct parts. https://arxiv.org/abs/2610.35322

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