{"paper":{"title":"Permutations of $\\mathbb{Z}^d$ with restricted movement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Strasser, Klaus Schmidt","submitted_at":"2015-10-05T09:01:44Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01068","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}