The number of lattice paths below a cyclically shifting boundary
Combinatorics
2007-12-20 v1
Abstract
We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical reflection argument. A refinement allows for the counting of paths with a specified number of corners. We also apply the result to examine paths dominated by periodic boundaries.
Cite
@article{arxiv.0712.3213,
title = {The number of lattice paths below a cyclically shifting boundary},
author = {J. Irving and A. Rattan},
journal= {arXiv preprint arXiv:0712.3213},
year = {2007}
}
Comments
20 pages, 13 figures