{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MXTU25X64MTTK2EEOCSNVY52BF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"725d0a08e5560a143910eb9a2d7e7d110cc60d0748495a732d758dc5194bebaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-21T15:27:24Z","title_canon_sha256":"11d5c449030d5d0fcc4378be50ac5ba9187e2956a0ab2858998b0084b5bd0537"},"schema_version":"1.0","source":{"id":"1103.4051","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4051","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4051v3","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4051","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"MXTU25X64MTT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MXTU25X64MTTK2EE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MXTU25X6","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:344329faf447878f9f4dfe956d133de2afda1fcd0babba13244ae6e5e39f371f","target":"graph","created_at":"2026-05-18T02:25:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Edita Pelantov\\'a, \\v{S}t\\v{e}p\\'an Starosta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-21T15:27:24Z","title":"Languages invariant under more symmetries: overlapping factors versus palindromic richness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4051","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:28bf4c259eaa23c6e03faa330cf11e7112a9ae72182bbc172df2dd94acd705b5","target":"record","created_at":"2026-05-18T02:25:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"725d0a08e5560a143910eb9a2d7e7d110cc60d0748495a732d758dc5194bebaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-21T15:27:24Z","title_canon_sha256":"11d5c449030d5d0fcc4378be50ac5ba9187e2956a0ab2858998b0084b5bd0537"},"schema_version":"1.0","source":{"id":"1103.4051","kind":"arxiv","version":3}},"canonical_sha256":"65e74d76fee32735688470a4dae3ba094cd7e10bfa0d78e876ab883eb601817d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65e74d76fee32735688470a4dae3ba094cd7e10bfa0d78e876ab883eb601817d","first_computed_at":"2026-05-18T02:25:12.235557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:12.235557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7UuQrFanV/+EUsobFUKV0REMvcwVgcgGtWXMDd0iYCSTW+5dVHDKahzLUmsz0NYIx/tk3dkL5714HsZ8/PgxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:12.235997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4051","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28bf4c259eaa23c6e03faa330cf11e7112a9ae72182bbc172df2dd94acd705b5","sha256:344329faf447878f9f4dfe956d133de2afda1fcd0babba13244ae6e5e39f371f"],"state_sha256":"371a1d70b06499fe48e921dc3b0cf1824fc23fb120399e8ab9ad4c7990e96176"}