English

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.

Keywords

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

R2 v1 2026-06-22T00:25:53.915Z