Generating trees for permutations avoiding generalized patterns

Details Generating trees for permutations avoiding generalized patterns Generating trees for permutations avoiding generalized patterns

2007-07-31

arxiv.org/abs/0707.4633v1

Mathematics

Combinatorics

17 pages, to appear in Ann. Comb

Scientific paper

We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-M\'elou. We obtain refinements of known enumerative results and find new ones.

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