On the Longest Common Pattern Contained in Two or More Random Permutations

Abstract

We provide upper and lower bounds for the expected length $\mathbb{E}(L_{n,m})$ of the longest common pattern contained in $m$ random permutations of length $n$. We also address the tightness of the concentration of $L_{n,m}$ around $\mathbb{E}(L_{n,m})$.