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Explicit bounds for multidimensional linear recurrences with restricted coefficients |
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| Authors: | Kenneth S Berenhaut John D Foley |
| Institution: | Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, USA |
| Abstract: | This note employs path counting techniques to extend recent results on bounds for odd order linear recurrences to higher dimensions. The results imply optimal zero-free polydisks for multivariable power series with 0, 1 coefficients. Among the applications is a result that states that the optimal zero-free polydisk has radius approximately 1/(v+1), for large dimensions v. |
| Keywords: | Explicit bounds Multidimensional recurrences Multivariable generating functions Power series Restricted coefficients Growth rates Nonconstant coefficients Partial order |
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