# Counting walks in a quadrant: a unified approach via boundary value problems

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 3, page 749-777
- ISSN: 1435-9855

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topRaschel, Kilian. "Counting walks in a quadrant: a unified approach via boundary value problems." Journal of the European Mathematical Society 014.3 (2012): 749-777. <http://eudml.org/doc/277202>.

@article{Raschel2012,

abstract = {The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walk.},

author = {Raschel, Kilian},

journal = {Journal of the European Mathematical Society},

keywords = {lattice walk; counting generating function; boundary value problem; conformal mapping; Weierstrass elliptic function; Riemann surface; uniformization; lattice walk; counting generating function; boundary value problem; conformal mapping; Weierstrass elliptic function; Riemann surface; uniformization},

language = {eng},

number = {3},

pages = {749-777},

publisher = {European Mathematical Society Publishing House},

title = {Counting walks in a quadrant: a unified approach via boundary value problems},

url = {http://eudml.org/doc/277202},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Raschel, Kilian

TI - Counting walks in a quadrant: a unified approach via boundary value problems

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 3

SP - 749

EP - 777

AB - The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walk.

LA - eng

KW - lattice walk; counting generating function; boundary value problem; conformal mapping; Weierstrass elliptic function; Riemann surface; uniformization; lattice walk; counting generating function; boundary value problem; conformal mapping; Weierstrass elliptic function; Riemann surface; uniformization

UR - http://eudml.org/doc/277202

ER -

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