Menu
An ordered tree, also known as a plane tree or a planar tree, is defined recursively as having a root and an ordered set of subtrees. A \(3\)-zebra tree is an ordered tree where all edges connected to the root (called height \( 1 \)) are tricolored, as are all edges at odd height. The edges at even height are all black as usual.
In this paper, we show that the number of \(3\)-zebra trees with \( n \) edges is equal to the number of Schröder paths with bicolored level steps.