Generating trees for permutations avoiding generalized patterns

Preprint

31 July 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0707.4633

Abstract

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.

Keywords

PERMUTATIONS AVOIDING GENERALIZED
AVOIDING GENERALIZED PATTERNS
CONSTRUCT GENERATING
GENERATING TREES
ENTRY
TREES

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Version 1, 2007-07-31, ArXiv

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