Patterns in trees☆

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Abstract

We give a general formula for the number of occurrences of a pattern, or set of patterns, in the class of ordered (plane-planted) trees with a given number of edges. The proof is combinatorial. Many known enumerations of ordered and binary trees are special cases of this formula.

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A preliminary version of this paper was presented at the Ninth Colloquium on Trees in Algebra and Programming, Bordeaux, France (March 1984). This research was supported in part by the National Science Foundation under grant DCR 85-13417, and by the Fund for Research in Electronics, Computers and Communications administered by the Israeli Academy of Sciences and Humanities.

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