{"paper":{"title":"Characterization of Entropy for Spacing shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawoud Ahmadi Dastjerdi, Maliheh Dabbaghian Amiri","submitted_at":"2011-10-27T17:37:50Z","abstract_excerpt":"Suppose $P\\subseteq \\mathbb{N}$ and let $(\\Sigma_P,\\,\\sigma_P)$ be the space of a spacing shift. We show that if entropy $h_{\\sigma_P}=0$ then $(\\Sigma_P,\\,\\sigma_P)$ is proximal. Also $h_{\\sigma_P}=0$ if and only if $P=\\mathbb N\\setminus E$ where $E$ is an intersective set. Moreover, we show that\n  $h_{\\sigma_P}>0$ implies that $P$ is a $\\Delta^*$ set; and by giving a class of examples, we show that this is not a sufficient condition. Then there is enough results to solve question 5 given in [J. Banks et al., \\textit{Dynamics of Spacing Shifts}, Discrete Contin. Dyn. Syst., to appear.]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6144","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"}