{"paper":{"title":"Avoidability of circular formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Guilhem Gamard, Gwena\\\"el Richomme, Pascal Ochem, Patrice S\\'e\\'ebold","submitted_at":"2016-10-14T12:53:38Z","abstract_excerpt":"Clark has defined the notion of $n$-avoidance basis which contains the avoidable formulas with at most $n$ variables that are closest to be unavoidable in some sense. The family $C_i$ of circular formulas is such that $C_1=AA$, $C_2=ABA.BAB$, $C_3=ABCA.BCAB.CABC$ and so on. For every $i\\le n$, the $n$-avoidance basis contains $C_i$. Clark showed that the avoidability index of every circular formula and of every formula in the $3$-avoidance basis (and thus of every avoidable formula containing at most 3 variables) is at most 4. We determine exactly the avoidability index of these formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04439","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"}