Title: Protection Number in Plane Trees,
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.