论文标题
随机排列中预期的不同连续模式的预期数
The Expected Number of Distinct Consecutive Patterns in a Random Permutation
论文作者
论文摘要
令$π_n$为$ [n] $上的均匀选择的随机排列。利用分析两个重叠的连续$ k $ - permutations是订单同构的概率，我们表明，$π_n$中的不同连续模式的预期数为$ \ frac {n^2} {2} {2} {2} {1-o（1-o（1-o（1））$。这表明了一个事实，即随机排列将连续的模式接近完美。
Let $π_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, we show that the expected number of distinct consecutive patterns in $π_n$ is $\frac{n^2}{2}(1-o(1))$. This exhibits the fact that random permutations pack consecutive patterns near-perfectly.
