Permutations avoiding a pattern of length three under Mallows distributions. Issue 4 (26th December 2020)

• Record Type: Journal Article
• Authors: Pinsky, Ross G.
• Is Part Of: Random structures & algorithms. Volume 58:Issue 4(2021)
• Page Start: 676
• Page End: 690
• Publication Date: 2020-12-26
• Subjects: Mallows distribution -- pattern‐avoiding permutation -- pattern of length three -- random permutation; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20988
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern τ ∈ S 3 ∖ { 321 }, we obtain rather precise results on the asymptotic probability as n → ∞ that a permutation σ ∈ S n under the Mallows distribution with parameter q ∈ (0, 1) avoids the pattern. By a duality between the parameters q and 1 q, we also obtain rather precise results on the above probability for q > 1 and any pattern τ ∈ S 3 ∖ { 123 } .