Permutations avoiding a certain pattern of length three under Mallows distributions

Ross G. Pinsky

Published 2019-08-04Version 1

We consider permutations avoiding a certain pattern of length three under the family of Mallows distributions. In particular, we obtain rather precise bounds on the asymptotic probability as $n\to\infty$ that a permutation $\sigma\in S_n$ under the Mallows distribution with parameter $q\in(0,1)$ avoids the pattern 312. The same result also holds for permutations avoiding 231. And by a duality, the same type of result also holds for the pattern 213 or 132 under the Mallows distribution with parameter $q>1$.