Permutations avoiding a pattern of length three under Mallows distributions. Issue 4 (26th December 2020) - Pinsky, Ross G.
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 .