最长k -交替子序列长度的方差和渐近分布

Discrete Mathematics & Theoretical Computer Science Pub Date : 2021-07-26 DOI:10.46298/dmtcs.10296

Altar cCicceksiz, Yunus Emre Demirci, Umit Icslak

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引用次数: 0

摘要

我们得到了均匀随机排列中k个峰值数目方差的一个显式公式。然后用它来获得随机排列中最长的k交替子序列的长度方差的渐近公式。并证明了后一统计量的中心极限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences

We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random permutations. Also a central limit is proved for the latter statistic.

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Discrete Mathematics & Theoretical Computer Science

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