{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GHWEGWN3ZW5X3FTSIT5RO5GLUB","short_pith_number":"pith:GHWEGWN3","schema_version":"1.0","canonical_sha256":"31ec4359bbcdbb7d967244fb1774cba05e86271da4d2fbeabe80efe2cee44ff2","source":{"kind":"arxiv","id":"1706.00529","version":3},"attestation_state":"computed","paper":{"title":"Generalized non-crossing Partitions and Buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Julia Heller, Petra Schwer","submitted_at":"2017-06-02T00:50:38Z","abstract_excerpt":"For any finite Coxeter group $W$ of rank $n$ we show that the order complex of the lattice of non-crossing partitions $\\mathrm{NC}(W)$ embeds as a connected chamber subcomplex into a spherical building of type $A_{n-1}$. We use this to give a new proof of the fact that the non-crossing partition lattice in type $A_n$ is supersolvable for all $n$ and show that in case $B_n$, this is only the case if $n<4$. We also obtain a lower bound on the radius of the Hurwitz graph $H(W)$ in all types and re-prove that in type $A_n$ the radius is ${n \\choose 2}$."},"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":"1706.00529","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-02T00:50:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"728ff6dc3ecde976ef8513f8fd404e885779a0c2a2b300b765dcf582beedbdd9","abstract_canon_sha256":"b204d5e3e93c1482dd49cae8c7192ac6f9b63b8661ba1ae76fc88cb61022389b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:10.382400Z","signature_b64":"lrm6tZ9QF89lDIeXLbbalU2gjjsTkoPyj1dv1XNMQvmbGlQgHpVcVVrQ2Txc/7v8ooX+s5ug4/9ReeLFHNFmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ec4359bbcdbb7d967244fb1774cba05e86271da4d2fbeabe80efe2cee44ff2","last_reissued_at":"2026-05-18T00:15:10.381675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:10.381675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized non-crossing Partitions and Buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Julia Heller, Petra Schwer","submitted_at":"2017-06-02T00:50:38Z","abstract_excerpt":"For any finite Coxeter group $W$ of rank $n$ we show that the order complex of the lattice of non-crossing partitions $\\mathrm{NC}(W)$ embeds as a connected chamber subcomplex into a spherical building of type $A_{n-1}$. We use this to give a new proof of the fact that the non-crossing partition lattice in type $A_n$ is supersolvable for all $n$ and show that in case $B_n$, this is only the case if $n<4$. We also obtain a lower bound on the radius of the Hurwitz graph $H(W)$ in all types and re-prove that in type $A_n$ the radius is ${n \\choose 2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00529","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.00529","created_at":"2026-05-18T00:15:10.381802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00529v3","created_at":"2026-05-18T00:15:10.381802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00529","created_at":"2026-05-18T00:15:10.381802+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHWEGWN3ZW5X","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHWEGWN3ZW5X3FTS","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHWEGWN3","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB","json":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB.json","graph_json":"https://pith.science/api/pith-number/GHWEGWN3ZW5X3FTSIT5RO5GLUB/graph.json","events_json":"https://pith.science/api/pith-number/GHWEGWN3ZW5X3FTSIT5RO5GLUB/events.json","paper":"https://pith.science/paper/GHWEGWN3"},"agent_actions":{"view_html":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB","download_json":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB.json","view_paper":"https://pith.science/paper/GHWEGWN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00529&json=true","fetch_graph":"https://pith.science/api/pith-number/GHWEGWN3ZW5X3FTSIT5RO5GLUB/graph.json","fetch_events":"https://pith.science/api/pith-number/GHWEGWN3ZW5X3FTSIT5RO5GLUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB/action/storage_attestation","attest_author":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB/action/author_attestation","sign_citation":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB/action/citation_signature","submit_replication":"https://pith.science/pith/GHWEGWN3ZW5X3FTSIT5RO5GLUB/action/replication_record"}},"created_at":"2026-05-18T00:15:10.381802+00:00","updated_at":"2026-05-18T00:15:10.381802+00:00"}