Lattice path enumeration by formal schema (Q1197397)

This paper gives another formal description of Pólya's idea of picture writing. An unlabelled rooted plane tree is represented as a word of the free monoid generated by the alphabet \(t\), ), \((_ n,\;n=1,2,3,\dots\), by starting with \(D\) and using the substitution rules \(D\to(_ n D^ n)\) if \(n\) is the number of edges emanating from the vertex \(D\) and \(D\to t\) for a terminal point.