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It is a pure simplicial complex of dimension a-2, and its maximal faces are counted by the {\\sf rational Catalan number} \\Cat(x)=\\Cat(a,b):=\\frac{(a+b-1)!}{a!\\,b!}. The cases (a,b)=(n,n+1) and (a,b)=(n,kn+1) recover the classical associahedron and its \"Fuss-Catalan\" generalization studied by Athanasiadis-Tzanaki and"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.7286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-31T02:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"a6cfb9be27d3b73d87d4c5836e11452a96dcf4f07231229449d4c3023d64bf8d","abstract_canon_sha256":"b85ed44175767ceeb177ac6ca8dbf1d1eb88a8855b8d5d90e35d4ade57b8ec33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:07.302526Z","signature_b64":"P+zNdH4E7u9ij/ilUQ9+uGwQp/9fgIrOnjuVDsqlKbhn2ruOTFa8JjXR841S07xpy/oXMaAKJK8J9hG0ftA+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b81f95acea0cd2b9eea40c4709741a54d14b276627b9d465edb50aa72e3004bd","last_reissued_at":"2026-05-18T03:22:07.301717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:07.301717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational associahedra and noncrossing partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Drew Armstrong, Nathan Williams","submitted_at":"2013-05-31T02:38:05Z","abstract_excerpt":"Each positive rational number x>0 can be written uniquely as x=a/(b-a) for coprime positive integers 0<a<b. 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