Fixed points of 321-avoiding permutations

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 861-872, 2018.

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Abstract:

We describe the distribution of the number and location of the fixed points of permutations that avoid the pattern 321 via a bijection with rooted ordered trees on n+1 vertices. Using the local limit theorem for Galton-Watson trees, we are able to give an explicit description of the limit of this distribution.

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