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Fixed points of 321-avoiding permutations
Christopher Hoffman, Douglas Rizzolo, Erik Slivken · 2016-07-29 · via math.PR updates on arXiv.org

We describe the distribution of the number and location of the fixed points of permu- tations that avoid the pattern 321 via a bijection with rooted plane 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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