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Ziegler","submitted_at":"2011-09-26T12:47:04Z","abstract_excerpt":"Hohlweg and Lange (2007) and Santos (2004, unpublished) have found two different ways of constructing exponential families of realizations of the n-dimensional associahedron with normal vectors in {0,1,-1}^n, generalizing the constructions of Loday (2004) and Chapoton-Fomin-Zelevinsky (2002). We classify the associahedra obtained by these constructions modulo linear equivalence of their normal fans and show, in particular, that the only realization that can be obtained with both methods is the Chapoton-Fomin-Zelevinsky (2002) associahedron.\n  For the Hohlweg-Lange associahedra our classificati"},"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":"1109.5544","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-09-26T12:47:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"481ef3e513846dff492a36f9d4bc84fc825af5d6edc9389becda1ac708baa99d","abstract_canon_sha256":"ebefdc92ad4be45398ff148383cb454710f263bf55afc4ca79eed2a70e5d24c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:16.541490Z","signature_b64":"jIXS7NwHyzcspTN7WPF/W2L+Mv6PCN3+nKWwdDufzmUDqWSnR4qKC2kt/4lVlXIpCPe1uRaiWQAjPhLtyHC/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93fbd69f906307d523233e2ac99612d26af43164b35795112619d9b728bb3212","last_reissued_at":"2026-05-18T01:21:16.540719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:16.540719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Many non-equivalent realizations of the associahedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Cesar Ceballos, Francisco Santos, G\\\"unter M. 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