{"paper":{"title":"Computable F{\\o}lner monotilings and a theorem of Brudno II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikita Moriakov","submitted_at":"2015-10-13T19:34:31Z","abstract_excerpt":"A theorem of A.A. Brudno says that the Kolmogorov-Sinai entropy of a subshift X over $\\mathbb{N}$ with respect to an ergodic measure $\\mu$ equals the asymptotic Kolmogorov complexity of almost every word $\\omega$ in X. The purpose of this article is to extend this result to subshifts over computable groups that admit computable regular symmetric F{\\o}lner monotilings, which we introduce in this work. These monotilings are a special type of computable F{\\o}lner monotilings, which we defined earlier in order to extend the initial results of Brudno. For every $d \\in \\mathbb{N}$, the groups $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03833","kind":"arxiv","version":2},"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"}