Pattern avoidance in binary trees

Details Pattern avoidance in binary trees Pattern avoidance in binary trees

2008-09-02

arxiv.org/abs/0809.0488v2

Journal of Combinatorial Theory, Series A 117 (2010) 741-758

Mathematics

Combinatorics

19 pages, many images; published version

Scientific paper

This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf equivalence in which two tree patterns are equivalent if the respective n-leaf trees that avoid them are equinumerous. We investigate the equivalence classes combinatorially. Toward establishing bijective proofs of tree pattern equivalence, we develop a general method of restructuring trees that conjecturally succeeds to produce an explicit bijection for each pair of equivalent tree patterns.

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