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The Brownian limit of separable permutations. (English) Zbl 1430.60013
Summary: We study uniform random permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a “Brownian separable permuton”.

60C05 Combinatorial probability
05A05 Permutations, words, matrices
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