{"paper":{"title":"Computable F{\\o}lner monotilings and a theorem of Brudno I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikita Moriakov","submitted_at":"2015-09-25T19:53:03Z","abstract_excerpt":"The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over $\\mathbb{N}$ to the Kolmogorov complexity of words in X, to subshifts over computable groups that posses computable F{\\o}lner monotilings, which we introduce in this work. The classical examples of such groups are the groups $\\mathbb{Z}^d$ and the groups of upper-triangular matrices with integer entries. Following the work of B. Weiss we show that the class of such groups is closed under group extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07858","kind":"arxiv","version":3},"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"}