Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations |
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| Authors: | Christopher Hoffman Douglas Rizzolo Erik Slivken |
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| Affiliation: | 1. Department of Mathematics, University of Washington, Seattle, Washington;2. Department of Mathematical Sciences, University of Delaware, Newark, Delaware;3. Department of Mathematics, University of California, Davis, California |
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| Abstract: | Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017 |
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| Keywords: | pattern‐avoiding permutations Brownian Excursion fixed point distribution |
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