Counting Lattice Paths By Gessel Pairs
Combinatorics
2007-05-23 v1 Probability
Abstract
We count a large class of lattice paths by using factorizations of free monoids. Besides the classical lattice paths counting problems related to Catalan numbers, we give a new approach to the problem of counting walks on the slit plane (walks avoid a half line) that was first solved by Bousquet-M\'{e}lou and Schaeffer. We also solve a problem about walks in the half plane avoiding a half line by subsequently applying the factorizations of two different Gessel pairs, giving a generalization of a result of Bousquet-M\'{e}lou.
Keywords
Cite
@article{arxiv.math/0409238,
title = {Counting Lattice Paths By Gessel Pairs},
author = {Guoce Xin},
journal= {arXiv preprint arXiv:math/0409238},
year = {2007}
}
Comments
12 pages