Asymptotics of lattice walks via analytic combinatorics in several variables

  title={Asymptotics of lattice walks via analytic combinatorics in several variables},
  author={Stephen Melczer and Mark C. Wilson},
  journal={Discrete Mathematics \& Theoretical Computer Science},
International audience We consider the enumeration of walks on the two-dimensional non-negative integer lattice with steps defined by a finite set S ⊆ {±1, 0}2 . Up to isomorphism there are 79 unique two-dimensional models to consider, and previous work in this area has used the kernel method, along with a rigorous computer algebra approach, to show that 23 of the 79 models admit D-finite generating functions. In 2009, Bostan and Kauers used Pade ́-Hermite approximants to guess differential… 

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