Permutations avoiding a pattern of length three under Mallows distributions

2019/08/04 by Pinsky, Ross G.
#05A05 #60C05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1908.01382

Abstract

We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern τ∈ S₃-\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 \frac1q, we also obtain rather precise results on the above probability for q>1 and any pattern τ∈ S₃-\123\.

Related

• The probability of avoiding consecutive patterns in the Mallows distribution
• Classical patterns in Mallows permutations
• Patterns in random permutations avoiding some sets of multiple patterns
• On the Cycle Structure of Mallows Permutations
• The Shape of Random Pattern-Avoiding Permutations