{"paper":{"title":"On Theta-palindromic Richness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Stepan Starosta","submitted_at":"2010-05-05T11:51:44Z","abstract_excerpt":"In this paper we study generalization of the reversal mapping realized by an arbitrary involutory antimorphism $\\Theta$. It generalizes the notion of a palindrome into a $\\Theta$-palindrome -- a word invariant under $\\Theta$. For languages closed under $\\Theta$ we give the relation between $\\Theta$-palindromic complexity and factor complexity. We generalize the notion of richness to $\\Theta$-richness and we prove analogous characterizations of words that are $\\Theta$-rich, especially in the case of set of factors invariant under $\\Theta$. A criterion for $\\Theta$-richness of $\\Theta$-episturmi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0722","kind":"arxiv","version":2},"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"}