## Miner, Samuel and Rizzolo, Douglas and Slivken, Erik - Asymptotic distribution of fixed points of pattern-avoiding involutions

dmtcs:3658 - Discrete Mathematics & Theoretical Computer Science, December 11, 2017, Vol. 19 no. 2, Permutation Patterns 2016 - https://doi.org/10.23638/DMTCS-19-2-5
Asymptotic distribution of fixed points of pattern-avoiding involutions

Authors: Miner, Samuel and Rizzolo, Douglas and Slivken, Erik

For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as well as all patterns of length 3. For monotone patterns we utilize the connection with standard Young tableaux with at most $k$ rows and involutions avoiding a monotone pattern of length $k$. For every pattern of length 3 we give the bivariate generating function with respect to fixed points for the involutions that avoid that pattern, and where applicable apply tools from analytic combinatorics to extract information about the limiting distribution from the generating function. Many well-known distributions appear.

Volume: Vol. 19 no. 2, Permutation Patterns 2016
Section: Permutation Patterns
Published on: December 11, 2017
Submitted on: May 16, 2017
Keywords: Mathematics - Combinatorics,Mathematics - Probability,60C05