Geodesic
Sufficient conditions of algebraicity of generating functions of the solutions of multidimensional difference equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 88-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study difference equations (recurrence relations) in rational lattice cones. It is found the relation between generating functions of the initial data and generating functions of the solutions of Cauchy problem for multidimensional difference equations. It is proved that condition of algebraicity (rationality) of generating functions of the initial data is sufficient condition of algebraicity (rationality) of generating functions of the solution.
Keywords: multidimensional difference equations; Cauchy problem; generating function. 
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T. I. Nekrasova. Sufficient conditions of algebraicity of generating functions of the solutions of multidimensional difference equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 88-96. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a6/

[1] E. K. Leinartas, A. P. Lyapin, “O ratsionalnosti mnogomernykh vozvratnykh stepennykh ryadov”, Zhurn. Sib. feder. un-ta, 2:4 (2009), 449–455

[2] T. I. Nekrasova, “Zadacha Koshi dlya mnogomernogo raznostnogo uravneniya v konusakh tselochislennoi reshetki”, Zhurn. Sib. feder. un-ta, 5:4 (2012), 576–580

[3] R. Stenli, Perechislitelnaya kombinatorika, Mir, M., 1990, 440 pp. | MR

[4] R. Stenli, Perechislitelnaya kombinatorika. Derevya, proizvodyaschie funktsii i simmetricheskie funktsii, Mir, M., 2009, 767 pp. | MR

[5] M. Bousquet-Mélou, M. Petkovšek, “Linear recurrences with constant coefficients: the multivariate case”, Discrete Mathematics, 225 (2000), 51–75 | DOI | MR

[6] A. de Moivre, “De fractionibus algebraicis radicalitate immunibus ad fractiones simpliciores reducendis, deque summandis terminis quarumdam serierum aequali intervallo a se distantibus”, Philosophical transactions, 32:1722/3 (1724), 176

[7] M. Forsberg, M. Passare, A. Tsikh, “Laurent Determinants and Arrangements of Hyperplane Amoebas”, Advances in Math., 151 (2000), 45–70 | DOI | MR