A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations

Christian Houdré; Chen Xu

A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations

Probability 2018-06-05 v2

Authors: Christian Houdré , Chen Xu

Abstract

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.

Keywords

longest common subsequence random permutation expected length lower bound i.i.d.

Cite

@article{arxiv.1703.07691,
  title  = {A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations},
  author = {Christian Houdré and Chen Xu},
  journal= {arXiv preprint arXiv:1703.07691},
  year   = {2018}
}

Comments

10 pages. Final version which is to appear in Electronic Journal of Combinatorics

A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations

Abstract

Keywords

Cite

Comments

Related papers