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arXiv · 1212.3265

On the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words

Christian Houdré·Jinyong Ma
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Abstract

We investigate the order of the $r$-th, $1\le r < +\infty$, central moment of the length of the longest common subsequence of two independent random words of size $n$ whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, a lower bound is shown to be of order $n^{r/2}$. This result complements a generic upper bound also of order $n^{r/2}$.

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Christian Houdré, Jinyong Ma. 2012-12-13. On the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words. https://arxiv.org/abs/1212.3265

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