On the dimension of systems of algebraic difference equations
arXiv:2004.01596 · doi:10.1016/j.aam.2020.102136
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.
28 pages, some corrections and more details added, mainly in Section 1