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Given an algebraic $\mathbf{Z}^{d}$ -action corresponding to a prime ideal of a Laurent ring of polynomials in several variables, we show how to find the smallest order $n+1$ of non-mixing.… Click to show full abstract
Given an algebraic $\mathbf{Z}^{d}$ -action corresponding to a prime ideal of a Laurent ring of polynomials in several variables, we show how to find the smallest order $n+1$ of non-mixing. It is known that this is determined by the non-mixing sets of size $n+1$ , and we show how to find these in an effective way. When the underlying characteristic is positive and $n\geq 2$ , we prove that there are at most finitely many classes under a natural equivalence relation. We work out two examples, the first with five classes and the second with 134 classes.
Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2017
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