Geodesic
The Cauchy problem for multidimensional difference equations in lattice cones
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 187-196

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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 in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.
Keywords: difference equation, fundamental solution, generating function, Dyck paths. 
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     title = {The {Cauchy} problem for multidimensional difference equations in lattice cones},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Alexander P. Lyapin; Sreelatha Chandragiri. The Cauchy problem for multidimensional difference equations in lattice cones. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 187-196. http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a5/