Towards a Combinatorial Understanding of Lattice Path Asymptotics
Combinatorics
2018-05-22 v4
Abstract
We provide a new strategy to compute the exponential growth constant of enumeration sequences counting walks in lattice path models restricted to the quarter plane. The bounds arise by comparison with half-planes models. In many cases the bounds are provably tight, and provide a combinatorial interpretation of recent formulas of Fayolle and Raschel (2012) and Bostan, Raschel and Salvy (2013). We discuss how to generalize to higher dimensions.
Cite
@article{arxiv.1305.7418,
title = {Towards a Combinatorial Understanding of Lattice Path Asymptotics},
author = {Samuel Johnson and Marni Mishna and Karen Yeats},
journal= {arXiv preprint arXiv:1305.7418},
year = {2018}
}
Comments
13 pages - technical correction from previous version