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.

中文翻译：

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关于代数差分方程组的维数

我们为代数差分方程组的解集引入了维数概念，用于在确定序列环中的解时测量自由度。这个数字不必是整数，但正如我们所展示的，它满足适用于维度概念的属性。我们还表明，差分单项式的维数由其指数集的覆盖密度给出。