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math.CO2025
Integrability of Combinatorial Riemann Boundary Value Problem and Lattice Walks Avoiding a Quadrant
Ruijie Xu
We introduce a general framework of matrix-form combinatorial Riemann boundary value problem (cRBVP) to characterize the integrability of functional equations arising in lattice wa…
math.CO2023
Combinatorial Insight of Riemann Boundary Value Problem in Lattice Walk Problems
Ruijie Xu
The enumeration of quarter-plane lattice walks with small steps is a classical problem in combinatorics. An effective approach is the kernel method, where the solution is derived b…
math.CO2019★ 1 cited
Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models
Nicholas R. Beaton, Aleksander L. Owczarek, Ruijie Xu
Lattice paths in the quarter plane have led to a large and varied set of results in recent years. One major project has been the classification of step sets according to the proper…