Walks in the quarter plane, genus zero case

Abstract

We use Galois theory of difference equations to study the nature of the generating series of (weighted) walks in the quarter plane with genus zero kernel curve. Using this approach, we prove that the generating series do not satisfy any nontrivial (possibly nonlinear) algebraic differential equation with rational coefficients.

Journal of Combinatorial Theory, Series A

References in corpus (4)

• Intervals in the greedy Tamari posets
• Counting quadrant walks via Tutte's invariant method
• On the nature of the generating series of walks in the quarter plane
• Length derivative of the generating series of walks confined in the quarter plane

Cited by in corpus (9)

• Intervals in the greedy Tamari posets
• Counting quadrant walks via Tutte's invariant method
• Length derivative of the generating series of walks confined in the quarter plane
• Enumeration of three-quadrant walks via invariants: some diagonally symmetric models
• On the nature of four models of symmetric walks avoiding a quadrant
• Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
• On the stationary distribution of reflected Brownian motion in a wedge: differential properties
• Differential algebraic generating series of weighted walks in the quarter plane
• Enumeration of three quadrant walks with small steps and walks on other M-quadrant cones