A combinatorial understanding of lattice path asymptotics

作者:Johnson Samuel; Mishna Marni*; Yeats Karen
来源:Advances in Applied Mathematics, 2018, 92: 144-163.
DOI:10.1016/j.aam.2017.08.001

摘要

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.

  • 出版日期2018-1

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