Christopher Hoffman, Douglas Rizzolo, Erik Slivken
Published 2014-06-19, updated 2015-06-12Version 2
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, and Miner and Pak as well as to understand many of the interesting phenomena that had previously gone unexplained.
Comments: 24 pages, The paper has been split into two parts to make the results more accessible. Part I contains results on limit shapes and fluctuations while Part II contains results on the asymptotic distribution of fixed points
Pattern-avoiding permutations and Brownian excursion, Part II: Fixed points
Increasing subsequences of linear size in random permutations and the Robinson-Schensted tableaux of permutons
Sequential Selection of a Monotone Subsequence from a Random Permutation
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