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arXiv · 1702.06816

Protection Number in Plane Trees

Clemens Heuberger·Helmut Prodinger
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Abstract

The protection number of a plane tree is the minimal distance of the root to a leaf; this definition carries over to an arbitrary node in a plane tree by considering the maximal subtree having this node as a root. We study the the protection number of a uniformly chosen random tree of size $n$ and also the protection number of a uniformly chosen node in a uniformly chosen random tree of size $n$. The method is to apply singularity analysis to appropriate generating functions. Additional results are provided as well.

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Clemens Heuberger, Helmut Prodinger. 2017-02-22. Protection Number in Plane Trees. https://doi.org/10.2298/aadm1702314h

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