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This result was previously established for the real reflection groups and it can be extended to the well-generated complex reflection group of type $G(d,1,n)$, for $d,n\\geq 3$, as well as to three exceptional groups, namely $G_{25},G_{26}$ and $G_{32}$, using a braid group argument. We thus conclude that the la"},"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":"1111.7172","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-30T14:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"2421eec60401d34e9ee63e63035fc6d7a7076de02e74b054cbd97779bf54a216","abstract_canon_sha256":"318c1cd1fb2524483d41c0dd13e1ffd0d0e7e6af9e7ea3400cebfadd918c2752"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:33.877332Z","signature_b64":"TjVlftGZJfB0b0oWOJ9xkwtObbp3Jqk9dDAxuMqhp31/i+bLRT1xJx2EStDlZ2JaKMhwOZJjnFw6wBLwqXMDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d4b2fe04a606b071d6ad43108c6177b260c5b4132b0a9076b8ee88de9ff085f","last_reissued_at":"2026-05-18T01:10:33.876768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:33.876768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle","submitted_at":"2011-11-30T14:13:07Z","abstract_excerpt":"In this article we prove that the lattice of noncrossing partitions is EL-shellable when associated with the well-generated complex reflection group of type $G(d,d,n)$, for $d,n\\geq 3$, or with the exceptional well-generated complex reflection groups which are no real reflection groups. 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