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arXiv · 1502.07893

Leaf-to-leaf distances in Catalan trees

Andrew M. Goldsborough·Jonathan M. Fellows·Matthew Bates·S. Alex Rautu·George Rowlands·Rudolf A. Römer
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Abstract

We study the average leaf-to-leaf path lengths on ordered Catalan tree graphs with $n$ nodes and show that these are equivalent to the average length of paths starting from the root node. We give an explicit analytic formula for the average leaf-to-leaf path length as a function of separation of the leaves and study its asymptotic properties. At the heart of our method is a strategy based on an abstract graph representation of generating functions.

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Andrew M. Goldsborough, Jonathan M. Fellows, Matthew Bates, S. Alex Rautu, George Rowlands, Rudolf A. Römer. 2015-02-27. Leaf-to-leaf distances in Catalan trees. https://doi.org/10.18642/jpamaa_7100121956

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