子划分极大化划分的极限形状
Limit Shape of Subpartition Maximizing Partitions
摘要：
这是一个暂时的说明回答了理查德斯坦利向我们提出的一个问题，我们证明了一个极限形状定理的分区的$n$，最大限度地提高了数量的子分区。极限形状和子分区数的增长率是明确的。关键思想是使用随机游动的大偏差估计，连同凸分析和Hardy-Ramanujan渐近。我们的极限形状一致Vershik的均匀随机分区的极限形状。
英文摘要：
This is an expository note answering a question posed to us by Richard Stanley, in which we prove a limit shape theorem for partitions of $n$ which maximize the number of subpartitions. The limit shape and the growth rate of the number of subpartitions are explicit. The key ideas are to use large deviations estimates for random walks, together with convex analysis and the Hardy-Ramanujan asymptotics. Our limit shape coincides with Vershik's limit shape for uniform random partitions.
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