The Infinite limit of random permutations avoiding patterns of length three

Permutations Avoiding Two Patterns of Length Three

We study permutations that avoid two distinct patterns of length three and any additional set of patterns. We begin by showing how to enumerate these permutations using generating trees, generalizing the work of Mansour [13]. We then find sufficient conditions for when the number of such permutations is given by a polynomial and answer a question of Egge [6]. Afterwards, we show how to use thes...

Refined Restricted Permutations Avoiding Subsets of Patterns of Length Three

Define Sk n(T ) to be the set of permutations of {1, 2, . . . , n} with exactly k fixed points which avoid all patterns in T ⊆ Sm. We enumerate Sk n(T ), T ⊆ S3, for all |T | ≥ 2 and 0 ≤ k ≤ n.

Avoiding Patterns of Length Three in Compositions and Multiset Permutations

We find generating functions for the number of compositions avoiding a single pattern or a pair of patterns of length three on the alphabet {1, 2} and determine which of them are Wilf-equivalent on compositions. We also derive the number of permutations of a multiset which avoid these same patterns and determine the Wilf-equivalence of these patterns on permutations of multisets. 2000 Mathemati...

Patterns in Random Permutations Avoiding

We consider a random permutation drawn from the set of 132-avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by n where λ(σ) is the length of σ plus the number of descents. The limit is not normal, and can be expressed as a functional of a Brownian excursion. Moments can be found by recursion.

Permutations avoiding two patterns of length