# Protection number in plane trees

CITATION: Heuberger, C. & Prodinger, H. 2017. Protection number in plane trees. Applicable Analysis and Discrete Mathematics, 11(2):314-326. doi:10.2298/AADM1702314H.

The original publication is available at http://pefmath.etf.rs/home.html

Article

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.