On the largest size of $(t,t+1,..., t+p)$-core partitions

Huan Xiong

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arXiv · 1410.2061

On the largest size of $(t,t+1,..., t+p)$-core partitions

Huan Xiong

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Abstract

In this paper we prove that Amdeberhan's conjecture on the largest size of $(t, t+1, t+2)$-core partitions is true. We also show that the number of $(t, t + 1, t + 2)$-core partitions with the largest size is $1$ or $2$ based on the parity of $t$. More generally, the largest size of $(t,t+1,..., t+p)$-core partitions and the number of such partitions with the largest size are determined.

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BibTeX RIS

Huan Xiong. 2015-01-07. On the largest size of $(t,t+1,..., t+p)$-core partitions. https://arxiv.org/abs/1410.2061

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