{"paper":{"title":"Languages invariant under more symmetries: overlapping factors versus palindromic richness","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":"2011-03-21T15:27:24Z","abstract_excerpt":"Factor complexity $\\mathcal{C}$ and palindromic complexity $\\mathcal{P}$ of infinite words with language closed under reversal are known to be related by the inequality $\\mathcal{P}(n) + \\mathcal{P}(n+1) \\leq 2 + \\mathcal{C}(n+1)-\\mathcal{C}(n)$ for any $n\\in \\mathbb{N}$\\,. Word for which the equality is attained for any $n$ is usually called rich in palindromes. In this article we study words whose languages are invariant under a finite group $G$ of symmetries. For such words we prove a stronger version of the above inequality. We introduce notion of $G$-palindromic richness and give several "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4051","kind":"arxiv","version":3},"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"}