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arXiv · 1510.01068

Permutations of $\mathbb{Z}^d$ with restricted movement

Klaus Schmidt·Gabriel Strasser
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Abstract

We investigate dynamical properties of the set of permutations of $\mathbb{Z}^d$ with restricted movement, i.e., permutations $\pi $ of $\mathbb{Z}^d$ such that $\pi (\mathbf{n})-\mathbf{n}$ lies, for every $\mathbf{n}\in \mathbb{Z}^d$, in a prescribed finite set $A\subset \mathbb{Z}^d$. For $d=1$, such permutations occur, for example, in restricted orbit equivalence, or in the calculation of determinants of certain bi-infinite multi-diagonal matrices. For $d\ge2$ these sets of permutations provide natural classes of examples of multidimensional shifts of finite type.

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Klaus Schmidt, Gabriel Strasser. 2015-10-05. Permutations of $\mathbb{Z}^d$ with restricted movement. https://arxiv.org/abs/1510.01068

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