# Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks

@article{Dreyfus2017DifferentialT, title={Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks}, author={T. Dreyfus and K. Raschel}, journal={arXiv: Combinatorics}, year={2017} }

We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain of the generating series are algebraic over the field of rational functions, while some others do not satisfy any algebraic differential equation with rational functions coefficients. Our techniques involve differential Galois theory for difference equations… CONTINUE READING

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