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Protection number in plane trees

Heuberger Clemens (Alpen-Adria-Universität Klagenfurt, Institut für Mathematik, Klagenfurt, Austria)
Prodinger Helmut (Stellenbosch University, Department of Mathematical Sciences, Stellenbosch, South Africa)

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.

Keywords: protected node, protection number, singularity analysis, plane tree