{"paper":{"title":"New results on pseudosquare avoidance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.FL","authors_text":"Jeffrey Shallit, Narad Rampersad, Pascal Ochem, Tim Ng","submitted_at":"2019-04-19T11:53:45Z","abstract_excerpt":"We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \\overline{x}$), and we completely classify which possibilities can occur. We consider avoiding $x p(x)$, where $p$ is any permutation of the underlying alphabet, and $x t(x)$, where $t$ is any transformation of the underlying alphabet. Finally, we prove the existence of an infinite binary word simultaneously avoiding all occurrences of $x h(x)$ for every nonerasing morphism $h$ and all sufficiently large words $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09157","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"}