We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the generating function of walks starting at a fixed point in this domain and ending anywhere within the domain. Intriguingly, the specialisation of this formula to walks starting in a fixed corner of the triangle shows that these are equinumerous to two-coloured Motzkin paths, and two-coloured three-candidate Ballot paths, in a strip of finite height.
@article{10_37236_4125,
author = {Paul R.G. Mortimer and Thomas Prellberg},
title = {On the number of walks in a triangular domain},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4125},
zbl = {1308.05010},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4125/}
}
TY - JOUR
AU - Paul R.G. Mortimer
AU - Thomas Prellberg
TI - On the number of walks in a triangular domain
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4125/
DO - 10.37236/4125
ID - 10_37236_4125
ER -
%0 Journal Article
%A Paul R.G. Mortimer
%A Thomas Prellberg
%T On the number of walks in a triangular domain
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4125/
%R 10.37236/4125
%F 10_37236_4125
Paul R.G. Mortimer; Thomas Prellberg. On the number of walks in a triangular domain. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4125
