Patterns in random permutations avoiding the pattern 321. Issue 2 (14th November 2018)

• Record Type: Journal Article
• Authors: Janson, Svante
• Is Part Of: Random structures & algorithms. Volume 55:Issue 2(2019)
• Page Start: 249
• Page End: 270
• Publication Date: 2018-11-14
• Subjects: patterns in permutations -- pattern‐avoiding permutations -- random permutations; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20806
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : We consider a random permutation drawn from the set of321 ‐avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by n m + ℓ where m is the length of σ and ℓ is the number of blocks in it. The limit is not normal, and can be expressed as a functional of a Brownian excursion.