A probabilistic approach to consecutive pattern avoiding in permutations

Abstract

We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this approach to give explicit upper and lower bounds on the number of permutations avoiding a consecutive pattern of length m. As a corollary, we obtain a simple proof of the CMP conjecture from Elizalde and Noy, regarding the most avoided pattern, recently proved by Elizalde. We also show that most of the patterns behave similarly to the least avoided one.