2020
DOI: 10.48550/arxiv.2004.01596
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On the dimension of systems of algebraic difference equations

Michael Wibmer

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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