Fixed points of 321-avoiding permutations

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.

References in corpus (1)

• Patterns in random permutations avoiding the pattern 132

Cited by in corpus (9)

• Patterns in random permutations avoiding the pattern 132
• A decorated tree approach to random permutations in substitution-closed classes
• Local convergence for permutations and local limits for uniform $\rho$-avoiding permutations with $|\rho |=3$
• Square permutations are typically rectangular
• Almost square permutations are typically square
• Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences
• Scaling limits of permutations avoiding long decreasing sequences
• A logical limit law for $231$-avoiding permutations
• Asymptotic distribution of fixed points of pattern-avoiding involutions