{"paper":{"title":"Open and closed factors of Arnoux-Rauzy words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luca Zamboni, Olga Parshina","submitted_at":"2018-10-12T12:17:47Z","abstract_excerpt":"A finite word $u$ is called closed if its longest repeated prefix has exactly two occurrences in $u,$ once as a prefix and once as a suffix. We study the function $f_x^c:\\mathbb N \\rightarrow \\mathbb N$ which counts the number of closed factors of each length in an infinite word $x.$ We derive an explicit formula for $f_x^c$ in case $x$ is an Arnoux-Rauzy word. As a consequence we prove that $\\liminf _{n\\rightarrow \\infty}f_x^c(n)=+\\infty.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05472","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"}