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arXiv · 1611.03840

The Length of the Longest Common Subsequence of Two Independent Mallows Permutations

Ke Jin
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Abstract

The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $π$ is proportional to $q^{l(π)}$ with $q > 0$ being a parameter and $l(π)$ the number of inversions in $π$. We prove a weak law of large numbers for the length of the longest common subsequences of two independent permutations drawn from the Mallows measure, when $q$ is a function of $n$ and $n(1-q)$ has limit in $\mathbb{R}$ as $n \to \infty$.

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Ke Jin. 2019-05-05. The Length of the Longest Common Subsequence of Two Independent Mallows Permutations. https://arxiv.org/abs/1611.03840

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