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arXiv · 2004.01596

On the dimension of systems of algebraic difference equations

Michael Wibmer
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Abstract

We introduce a notion of dimension for the solution set of a system of algebraic difference equations that measures the degrees of freedom when determining a solution in the ring of sequences. This number need not be an integer, but, as we show, it satisfies properties suitable for a notion of dimension. We also show that the dimension of a difference monomial is given by the covering density of its set of exponents.

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Michael Wibmer. 2020-04-03. On the dimension of systems of algebraic difference equations. https://doi.org/10.1016/j.aam.2020.102136

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