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Difference Equations and Generating Functions for some Lattice Path Problems
(Сибирский федеральный университет. Siberian Federal University, 2019-10)
An identity for generating functions is proved in this paper. A novel method to compute the number of restricted lattice paths is developed on the basis of this identity. The method employs a difference equation with ...
The Cauchy Problem for Multidimensional Difference Equations in Lattice Cones
(Сибирский федеральный университет. Siberian Federal University, 2020-03)
We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula ...