Linear recurrences with constant coefficients:: the multivariate case

While in the univariate case solutions of linear recurrences with constant coefficients have rational generating functions, we show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-finite but not algebraic, and even non-D-finite. (C) 2000 Published by Elsevier Science B.V. All rights reserved.