{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PUGBAV277673QMWBGYRR4K32FL","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":"6ff3a2ec1d49b2564e03dfe5e27cd84b4cc7eb548a8cb02169a75c4d14ad03fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-28T09:44:15Z","title_canon_sha256":"37039ccaa53e876f9261daecb099dc7599e1c45f92a07bf5a0d75d9d1df20ebb"},"schema_version":"1.0","source":{"id":"1806.10852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10852","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10852v1","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10852","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"pith_short_12","alias_value":"PUGBAV277673","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PUGBAV277673QMWB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PUGBAV27","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:0ccef0d8940f111df8c9d24ca36b29ecbd510aff0f2a980196fec80ee26f5c9c","target":"graph","created_at":"2026-05-18T00:12:07Z","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":"The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias, Proudfoot, and Wakefield [{\\it Adv. Math. 2016}]. Let $U_{m,d}$ denote the uniform matroid of rank $d$ on a set of $m+d$ elements. Gedeon, Proudfoot, and Young [{\\it J. Combin. Theory Ser. A, 2017}] pointed out that they can derive an explicit formula of the Kazhdan-Lusztig polynomials of $U_{m,d}$ using equivariant Kazhdan-Lusztig polynomials. In this paper we give two alternative explicit formulas, which allow us to prove the real-rootedness of the Kazhdan-Lusztig polynomials of $U_{m,d}$ for $2\\leq m\\leq 15$ and all $d$'s.","authors_text":"Alice L.L. Gao, Arthur L.B. Yang, Linyuan Lu, Matthew H.Y. Xie, Philip B. Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-28T09:44:15Z","title":"The Kazhdan-Lusztig polynomials of uniform matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10852","kind":"arxiv","version":1},"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":"sha256:3668b1f9065762f095814f88edaa46abfa894f3d8a30060fbfd427f492623f3b","target":"record","created_at":"2026-05-18T00:12:07Z","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":"6ff3a2ec1d49b2564e03dfe5e27cd84b4cc7eb548a8cb02169a75c4d14ad03fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-28T09:44:15Z","title_canon_sha256":"37039ccaa53e876f9261daecb099dc7599e1c45f92a07bf5a0d75d9d1df20ebb"},"schema_version":"1.0","source":{"id":"1806.10852","kind":"arxiv","version":1}},"canonical_sha256":"7d0c10575fffbfb832c136231e2b7a2acc07e2d1f2a8642a3e19551548561036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d0c10575fffbfb832c136231e2b7a2acc07e2d1f2a8642a3e19551548561036","first_computed_at":"2026-05-18T00:12:07.758237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:07.758237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ABS5ya5bjYfQbZaCG5vohJ5pGStFPfpsChHC0HKespNdYx53DPvw5C9h51T6wK/vbBzCiWkkeTixJEny/PGLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:07.758708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3668b1f9065762f095814f88edaa46abfa894f3d8a30060fbfd427f492623f3b","sha256:0ccef0d8940f111df8c9d24ca36b29ecbd510aff0f2a980196fec80ee26f5c9c"],"state_sha256":"09ab3bc59b14c6689184e84a26c3633890defa375843c224788fbd7e515bd7f7"}