New versions of Suen's correlation inequality
proceedings of the eighth international conference on Random structures and algorithms
On the number of permutations avoiding a given pattern
Journal of Combinatorial Theory Series A
Consecutive patterns in permutations
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Excluded permutation matrices and the Stanley-Wilf conjecture
Journal of Combinatorial Theory Series A
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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.