A probabilistic approach to consecutive pattern avoiding in permutations

DOI10.1016/J.JCTA.2013.02.004zbMATH Open1277.05006arXiv1208.5366OpenAlexW2088569908MaRDI QIDQ385031

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Publication date: 29 November 2013

Published in: (Search for Journal in Brave)

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 idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern of length m. As a corollary, we obtain a simple proof of the CMP conjecture, regarding the most avoided pattern, recently shown by Elizalde. Finally, we also show that most of the patterns behave similar to the least avoided one.

Full work available at URL: https://arxiv.org/abs/1208.5366

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