Enumeration of three quadrant walks with small steps and walks on other M-quadrant cones
Andrew Elvey Price
Abstract:We address the enumeration of walks with small steps conned to a two-dimensional cone, for example the quarter plane, three-quarter plane or the slit plane. In the quarter plane case, the solutions for unweighted step-sets are already well understood, in the sense that it is known precisely for which cases the generating function is algebraic, D-nite or D-algebraic, and exact integral expressions are known in all cases. We derive similar results in a much more general setting: we enumerate walks on an M -quadr… Show more
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