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math.CO2013★ 16 cited
A human proof of Gessel's lattice path conjecture
Alin Bostan, Irina Kurkova, Kilian Raschel
Gessel walks are lattice paths confined to the quarter plane that start at the origin and consist of unit steps going either West, East, South-West or North-East. In 2001, Ira Gess…
math.CO2013★ 14 cited
New steps in walks with small steps in the quarter plane
Irina Kurkova, Kilian Raschel
In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite ser…