{"paper":{"title":"Describtion of normal basis of boundary algebras and factor languages of small growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. L. Chernyatiev (HSE), Ariel, A. Ya. Belov (BIU, Mipt)","submitted_at":"2016-02-10T20:40:29Z","abstract_excerpt":"Let $A$ be an algebra with fixed set of generators $a_1,\\dots,a_s$. $V_A(n)$ be dimension of the space, generated by worlds of length $\\le n$ over $a_i$, $T_A(n)=V_A(n)-V_A(n-1)$. If $T_A(n)<\\mbox{Const}$, algebra $A$ is a {\\it boundary algebra}. We describe a normal basis of boundary algebras, i.e. algebras with small growth.\n  Let $\\cal L$ be a factor language over alphabet $\\cal A$. {\\it Growth function} $T_{\\cal L}(n)$ is number of subwords $\\cal L$ of degree $n$. We describe factor languages of small growth such that $T_{\\cal L}(n)\\le n+\\mbox{const}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03510","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"}