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arXiv · 1405.2175

Average Size of a Self-conjugate (s, t)-Core Partition

William Y. C. Chen·Harry H. Y. Huang·Larry X. W. Wang
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Abstract

Armstrong, Hanusa and Jones conjectured that if $s,t$ are coprime integers, then the average size of an $(s,t)$-core partition and the average size of a self-conjugate $(s,t)$-core partition are both equal to $\frac{(s+t+1)(s-1)(t-1)}{24}$. Stanley and Zanello showed that the average size of an $(s,s+1)$-core partition equals $\binom{s+1}{3}/2$. Based on a bijection of Ford, Mai and Sze between self-conjugate $(s,t)$-core partitions and lattice paths in $\lfloor \frac{s}{2} \rfloor\times \lfloor \frac{t}{2}\rfloor$ rectangle, we obtain the average size of a self-conjugate $(s,t)$-core partition as conjectured by Armstrong, Hanusa and Jones.

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William Y. C. Chen, Harry H. Y. Huang, Larry X. W. Wang. 2014-05-09. Average Size of a Self-conjugate (s, t)-Core Partition. https://arxiv.org/abs/1405.2175

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