On the Longest Common Subsequence of Conjugation Invariant Random Permutations

Kammoun, Slim (2020) On the Longest Common Subsequence of Conjugation Invariant Random Permutations. The Electronic Journal of Combinatorics, 27 (4). ISSN 1077-8926

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Abstract

Bukh and Zhou conjectured that the expectation of the length of the longest common subsequence of two i.i.d random permutations of size n is greater than √ n . We prove in this paper that there exists a universal constant n 1 such that their conjecture is satisfied for any pair of i.i.d random permutations of size greater than n 1 with distribution invariant under conjugation. More generally, in the case where the laws of the two permutations are not necessarily the same, we give a lower bound for the expectation. In particular, we prove that if one of the permutations is invariant under conjugation and with a good control of the expectation of the number of its cycles, the limiting fluctuations of the length of the longest common subsequence are of Tracy-Widom type. This result holds independently of the law of the second permutation.

Item Type:
Journal Article
Journal or Publication Title:
The Electronic Journal of Combinatorics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
ID Code:
148518
Deposited By:
Deposited On:
26 Oct 2020 13:20
Refereed?:
Yes
Published?:
Published
Last Modified:
20 Nov 2020 07:26