Geodesic
A note on the expected length of the longest common subsequences of two i.i.d. random permutations
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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We address a question and a conjecture on the expected length of the longest common subsequences of two i.i.d. random permutations of $[n]:=\{1,2,...,n\}$. The question is resolved by showing that the minimal expectation is not attained in the uniform case. The conjecture asserts that $\sqrt{n}$ is a lower bound on this expectation, but we only obtain $\sqrt[3]{n}$ for it.
DOI : 10.37236/6974
Classification : 05A05, 60C05
Mots-clés : random permutation, longest common subsequence 
@article{10_37236_6974,
     author = {Christian Houdr\'e and Chen Xu},
     title = {A note on the expected length of the longest common subsequences of two i.i.d. random permutations},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {2},
     doi = {10.37236/6974},
     zbl = {1391.05010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6974/}
}
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Christian Houdré; Chen Xu. A note on the expected length of the longest common subsequences of two i.i.d. random permutations. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/6974

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