On the longest k-alternating subsequence
Igor Pak, Robin Pemantle
TL;DR
This paper investigates the length of the longest k-alternating subsequence in a random permutation, establishing its asymptotic behavior as approximately two-thirds of (n-k).
Contribution
It provides a new asymptotic result for the length of the longest k-alternating subsequence in random permutations.
Findings
Longest k-alternating subsequence length asymptotic to 2(n-k)/3
Asymptotic behavior established for large permutations
Advances understanding of permutation pattern structures
Abstract
We show that the longest k-alternating substring of a random permutation has length asymptotic to 2 (n-k) / 3.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Methods and Mixture Models · Stochastic processes and statistical mechanics · Advanced Combinatorial Mathematics