Generating functions for plateaus in Motzkin paths
Combinatorics
2011-09-16 v1
Abstract
A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for plateaus in Motzkin paths, then generalize to longer plateaus. We conclude by describing a further generalization: a continued fraction form from which one can easily derive new multivariate generating functions for various kinds of path statistics. Several examples of generating functions are given using this technique.
Keywords
Cite
@article{arxiv.1109.3273,
title = {Generating functions for plateaus in Motzkin paths},
author = {Dan Drake and Ryan Gantner},
journal= {arXiv preprint arXiv:1109.3273},
year = {2011}
}