{"paper":{"title":"On arithmetic index in the generalized Thue-Morse word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Olga Parshina","submitted_at":"2018-11-09T12:40:41Z","abstract_excerpt":"Let $q$ be a positive integer. Consider an infinite word $\\omega=w_0w_1w_2\\cdots$ over an alphabet of cardinality $q$. A finite word $u$ is called an arithmetic factor of $\\omega$ if $u=w_cw_{c+d}w_{c+2d}\\cdots w_{c+(|u|-1)d}$ for some choice of positive integers $c$ and $d$. We call $c$ the initial number and $d$ the difference of $u$. For each such $u$ we define its arithmetic index by $\\lceil\\log_q d\\rceil$ where $d$ is the least positive integer such that $u$ occurs in $\\omega$ as an arithmetic factor with difference $d$. In this paper we study the rate of growth of the arithmetic index of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03884","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"}