Geodesic
Riordan's Arrays and Two-dimensional Difference Equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 210-220

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We describe of rational Riordan's arrays appearing in combinatorial analysis in terms of solutions of a Cauchy problem for a two-dimensional difference equation. The asymptotics of such arrays has been investigated.
Keywords: Riordan's arrays, multidimensional difference equations, Cauchy problem, the amoeba of a characteristic polynomial. 
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Alexander P. Lyapin. Riordan's Arrays and Two-dimensional Difference Equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 210-220. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a8/