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Singularity Analysis Via the Iterated Kernel Method

Published online by Cambridge University Press:  10 June 2014

STEPHEN MELCZER
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail: srm9@sfu.ca, mmishna@sfu.ca)
MARNI MISHNA
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail: srm9@sfu.ca, mmishna@sfu.ca)

Abstract

In the quarter plane, five lattice path models with unit steps have resisted the otherwise general approach featured in recent works by Fayolle, Kurkova and Raschel. Here we consider these five models, called the singular models, and prove that the univariate generating functions marking the number of walks of a given length are not D-finite. Furthermore, we provide exact and asymptotic enumerative formulas for the number of such walks, and describe an efficient algorithm for exact enumeration.

Type
Paper
Copyright
Copyright © Cambridge University Press 2014 

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