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2014•ISRN CombinatoricsOpen access

Noncontiguous Pattern Containment in Binary Trees

Lara Pudwell, Connor Scholten, Tyler Schrock, Alexa Serrato

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Abstract

We consider the enumeration of binary trees containing noncontiguous binary tree patterns. First, we show that any two ℓ -leaf binary trees are contained in the set of all n -leaf trees the same number of times. We give a functional equation for the multivariate generating function for number of n -leaf trees containing a specified number of copies of any path tree, and we analyze tree patterns with at most 4 leaves. The paper concludes with implications for pattern containment in permutations.

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What this paper is about

We consider the enumeration of binary trees containing noncontiguous binary tree patterns. First, we show that any two ℓ -leaf binary trees are contained in the set of all n -leaf trees the same number of times. We give a functional equation for the multivariate generating function for number of n -leaf trees containing a specified number of copies of any path tree, and we analyze tree patterns with at most 4 leaves. The paper concludes with implications for pattern containment in permutations.

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Available abstract

We consider the enumeration of binary trees containing noncontiguous binary tree patterns. First, we show that any two ℓ -leaf binary trees are contained in the set of all n -leaf trees the same number of times. We give a functional equation for the multivariate generating function for number of n -leaf trees containing a specified number of copies of any path tree, and we analyze tree patterns with at most 4 leaves. The paper concludes with implications for pattern containment in permutations.

Key concepts: Binary number, Binary tree, Tree (set theory), Path (computing), Enumeration, Computer science, Algorithm, Mathematics

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