{"paper":{"title":"Growth degree classification for finitely generated semigroups of integer matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jason P. Bell, Kevin G. Hare, Michael Coons","submitted_at":"2014-10-21T02:05:59Z","abstract_excerpt":"Let $\\mathcal{A}$ be a finite set of $d\\times d$ matrices with integer entries and let $m_n(\\mathcal{A})$ be the maximum norm of a product of $n$ elements of $\\mathcal{A}$. In this paper, we classify gaps in the growth of $m_n(\\mathcal{A})$; specifically, we prove that $\\lim_{n\\to\\infty} \\log m_n(\\mathcal{A})/\\log n\\in\\mathbb{Z}_{\\geqslant 0}\\cup\\{\\infty\\}.$ This has applications to the growth of regular sequences as defined by Allouche and Shallit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5519","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"}