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Conference Papers Year : 2022

Enumeration of walks with small steps avoiding a quadrant

Andrew Elvey Price
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Abstract

We address the enumeration of walks with weighted small steps avoiding a quadrant. In particular we give an exact, integral-expression solution for the generating function C(x, y; t) counting these walks by length and end-point. Moreover, we determine precisely when this generating function is algebraic, D-finite or D-algebraic with respect to x, showing that this complexity is the same as for walks in the quarterplane with the same starting point, as long as the starting point (p, q) of the walks lies in the quarter plane then. Finally, we give an integral-free expression for the solution in the cases where (p, q) lies just outside the quarter plane, that is p = 0 or q = 0 with our convention, proving a conjecture of Raschel and Trotignon.
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Dates and versions

hal-03880904 , version 1 (01-12-2022)

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  • HAL Id : hal-03880904 , version 1

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Andrew Elvey Price. Enumeration of walks with small steps avoiding a quadrant. FPSAC 2022, 2022, Bangalore, India. ⟨hal-03880904⟩
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