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arXiv · 1607.08742

Fixed points of 321-avoiding permutations

Christopher Hoffman·Douglas Rizzolo·Erik Slivken
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Abstract

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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Christopher Hoffman, Douglas Rizzolo, Erik Slivken. 2016-07-29. Fixed points of 321-avoiding permutations. https://doi.org/10.1090/proc%2F14299

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