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arXiv · 2305.15899

Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions

Yetong Sha·Huan Xiong
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Abstract

In 2016, Nath and Sellers proposed a conjecture regarding the precise largest size of ${(s,ms-1,ms+1)}$-core partitions. In this paper, we prove their conjecture. One of the key techniques in our proof is to introduce and study the properties of generalized-$β$-sets, which extend the concept of $β$-sets for core partitions. Our results can be interpreted as a generalization of the well-known result of Yang, Zhong, and Zhou concerning the largest size of $(s,s+1,s+2)$-core partitions.

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Yetong Sha, Huan Xiong. 2024-03-05. Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions. https://arxiv.org/abs/2305.15899

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