{"paper":{"title":"Pattern Avoidability with Involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.FL","authors_text":"Bastian Bischoff (Institute for Formal Methods in Computer Science, Dirk Nowotka (Institute for Formal Methods in Computer Science, Universit\\\"at Stuttgart)","submitted_at":"2011-08-18T03:52:46Z","abstract_excerpt":"An infinte word  w  avoids a pattern  p  with the involution  t  if there is no substitution for the variables in  p  and no involution  t  such that the resulting word is a factor of  w.   We investigate the avoidance of patterns with respect to the size of the alphabet. For example, it is shown that the pattern  a t(a) a  can be avoided over three letters but not two letters, whereas it is well known that  a a a  is avoidable over two letters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3622","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"}