{"paper":{"title":"Shift Radix Systems - A Survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\\"org M. Thuswaldner, Peter Kirschenhofer","submitted_at":"2013-12-02T09:31:20Z","abstract_excerpt":"Let $d\\ge 1$ be an integer and ${\\bf r}=(r_0,\\dots,r_{d-1}) \\in \\mathbf{R}^d$. The {\\em shift radix system} $\\tau_\\mathbf{r}: \\mathbb{Z}^d \\to \\mathbb{Z}^d$ is defined by $$ \\tau_{{\\bf r}}({\\bf z})=(z_1,\\dots,z_{d-1},-\\lfloor {\\bf r} {\\bf z}\\rfloor)^t \\qquad ({\\bf z}=(z_0,\\dots,z_{d-1})^t). $$ $\\tau_\\mathbf{r}$ has the {\\em finiteness property} if each ${\\bf z} \\in \\mathbb{Z}^d$ is eventually mapped to ${\\bf 0}$ under iterations of $\\tau_\\mathbf{r}$. In the present survey we summarize results on these nearly linear mappings. We discuss how these mappings are related to well-known numeration sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0386","kind":"arxiv","version":1},"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"}