A combinatorial understanding of lattice path asymptotics.


We provide a combinatorial derivation of the exponential growth constant for counting sequences of lattice path models restricted to the quarter plane. The values arise as bounds from analysis of related half planes models. We give explicit formulas, and the bounds are provably tight. The strategy is easily generalizable to cones in higher dimensions, and has implications for random generation.

Advances in Applied Mathematics
Samuel Johnson
PhD Candidate, Resource and Environmental Management