Christopher Hoffman, Douglas Rizzolo, Erik Slivken
Published 2015-06-12Version 1
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 fixed points of both 123- and 231-avoiding permutations. We find an exact description for a scaling limit of the empirical distribution of fixed points in term of Brownian excursion. This builds on the connections between pattern-avoiding permutations and Brownian excursion developed in Part I of this series and strengthens the recent results of Elizalde (2012) and Miner and Pak (2014) on fixed points of pattern-avoiding permutations.
Comments: 35 pages. This is Part II of the series on pattern-avoiding permutations and Brownian excursion. Part I (arXiv:1406.5156v2) contains results on limit shapes and fluctuations. The two parts were initially combined (arXiv:1406.5156v1), but were split to make the results more accessible
Pattern-avoiding permutations and Brownian excursion Part I: Shapes and fluctuations
Phase transition for parking blocks, Brownian excursion and coalescence
On the Brownian separable permuton
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