{"paper":{"title":"Characterization algorithms for shift radix systems with finiteness property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mario Weitzer","submitted_at":"2014-01-21T10:55:15Z","abstract_excerpt":"For a natural number d and a d-dimensional real vector r let Tau(r) denote the (d-dimensional) shift radix system associated with r. Tau(r) is said to have the finiteness property iff all orbits of Tau(r) end up in the zero vector; the set of all corresponding parameters r is denoted by DN(d), whereas D(d) consists of those parameters r for which all orbits are eventually periodic. DN(d) has a very complicated structure even for d=2. In the present paper two algorithms are presented which allow the characterization of the intersection of DN(d) and any closed convex hull of finitely many interi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5259","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"}