Analytic variations on the common subexpression problem
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Analytic Combinatorics
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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.