Permutations avoiding a pattern of length three under Mallows distributions
Ross G. Pinsky · Random Structures and Algorithms · 2020
Abstract We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern , we obtain rather precise results on the asymptotic probability as n → ∞ that a permutation under the Mallows distribution with parameter q ∈ (0, 1) avoids the pattern. By a duality between the parameters q and , we also obtain rather precise results on the above probability for q > 1 and any pattern .