{"paper":{"title":"Infinite words rich and almost rich in generalized palindromes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita Pelantov\\'a, \\v{S}t\\v{e}p\\'an Starosta","submitted_at":"2011-02-19T20:47:34Z","abstract_excerpt":"We focus on $\\Theta$-rich and almost $\\Theta$-rich words over a finite alphabet $\\mathcal{A}$, where $\\Theta$ is an involutive antimorphism over $\\mathcal{A}^*$. We show that any recurrent almost $\\Theta$-rich word $\\uu$ is an image of a recurrent $\\Theta'$-rich word under a suitable morphism, where $\\Theta'$ is again an involutive antimorphism. Moreover, if the word $\\uu$ is uniformly recurrent, we show that $\\Theta'$ can be set to the reversal mapping. We also treat one special case of almost $\\Theta$-rich words. We show that every $\\Theta$-standard words with seed is an image of an Arnoux-R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4023","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"}