18 citations · 137 across the 90 of their papers we have counts for
99 papers
Grand Motzkin paths and -trees -- a simple bijection
Helmut Prodinger
A well-known bijection between Motzkin paths and ordered trees with outdegree always , is lifted to Grand Motzkin paths (the nonnegativity is dropped) and an ordered list of…
Peakless Motzkin paths of bounded height
Helmut Prodinger
There was recent interest in Motzkin paths without peaks (peak: up-step followed immediately by down-step); additional results about this interesting family is worked out. The new…
S-Motzkin paths with catastrophes and air pockets
Helmut Prodinger
So called -Motzkin paths are combined the concepts `catastrophes' and `air pockets. The enumeration is done by properly set up bivariate generating functions which can be extend…
Counting edges according to edge-type in -ary trees
Helmut Prodinger
Using the Lagrange inversion formula, -ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).
Enumeration of partial Lukasiewicz paths
Jean-Luc Baril, Helmut Prodinger
Łukasiewicz paths are lattice paths in starting at the origin, ending on the -axis, and consisting of steps in the set . We give generating func…
Partial Skew Motzkin Paths
Helmut Prodinger
Motzkin paths consist of up-steps, down-steps, level-steps, and never go below the -axis. They return to the -axis at the end. The concept of skew Dyck path \cite{Deutsch-ita…