关于Plancherel测度集中在多少个Fibonacci词上
On how many Fibonacci words is the Plancherel measure concentrated
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中文总结 AI 辅助
研究Young-Fibonacci图中Plancherel测度在词集上的集中性，分析其熵和集中所需最少词数的渐近行为。
中文摘要 AI 辅助
在数字和为$n$的由1和2组成的词集合$\mathbb{YF}_n$上，我们考虑概率分布$\mu_P$，它对应于Young-Fibonacci图中路径上的Plancherel测度。我们研究随着$n$增长，分布$\mu_P$的熵以及$\mu_P$几乎完全集中所需的最少词数的渐近行为。
英文摘要
On the set $\mathbb{YF}_n$ of words in $1$ and $2$ with digit sum $n$, we consider the probability distribution $μ_P$, corresponding to the Plancherel measure on paths in the Young--Fibonacci graph. We study the asymptotics as $n$ grows of the entropy of the distribution $μ_P$ and of the minimum number of words on which $μ_P$ is almost entirely concentrated.
