Armstrong猜想关于同时核划分的Catalan情形
The Catalan case of Armstrong's conjecture on simultaneous core partitions
摘要：
D. Armstrong预测同时是$s$ -核心和$t$ -核心的分区的平均大小，其中$s$和$t$互质。我们的目标是证明这个猜想时，$t=s+1$。这些同步$(s,s+1)$核心分区由Catalan数枚举，具有平均大小$\binom{s+1}{3}/2$ .
英文摘要：
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simultaneously an $s$-core and a $t$-core, where $s$ and $t$ are coprime. Our goal is to prove this conjecture when $t=s+1$. These simultaneous $(s,s+1)$-core partitions, which are enumerated by Catalan numbers, have average size $\binom{s+1}{3}/2$.
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