Completion of the Wilf-Classification of 3-5 Pairs Using Generating Trees

A permutation is said to avoid the permutation if no subsequence in has the same order relations as . Two sets of permutations 1 and 2 are Wilfequivalent if, for all n, the number of permutations of length n avoiding all of the permutations in 1 equals the number of permutations of length n avoiding all of the permutations in 2. Using generating trees, we complete the problem of finding all Wilf-equivalences among pairs of permutations of which one has length 3 and the other has length 5 by proving that {123, 32541} is Wilf-equivalent to {123, 43251} and that {123, 42513} is Wilf-equivalent to {132, 34215}. In addition, we provide generating trees for fourteen other pairs, among which there are two examples of pairs that give rise to isomorphic generating trees.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Mark Lipson
• Keywords: COMBINATORICS 2006, Isomorphic Generating Trees, Order Relations, Permutations