{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5Z2DW74NWIJQIQLTI5F5Y4HQG5","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":"75e5345a841e68f10cb58500dfecb4306607b6ba41ab04b60a3b9f1d484b53ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T04:35:01Z","title_canon_sha256":"a78a1b67629bcea79852bfdc3d5140835c99dc60a1f81c74bf5a8d5961ae1d59"},"schema_version":"1.0","source":{"id":"1311.3014","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3014","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3014v2","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3014","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2DW74NWIJQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2DW74NWIJQIQLT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2DW74N","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:f5f94128ce3561552c3eda52a21ad939e43232bc6b85560da429296d7f423cb7","target":"graph","created_at":"2026-05-18T02:43:52Z","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":"A Peterson variety is a subvariety of the flag variety $G/B$ which appears in the construction of the quantum cohomology of partial flag varieties. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type $A$ Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives Monk's rule and Giambelli's formula for all Lie types.","authors_text":"Elizabeth Drellich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T04:35:01Z","title":"Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3014","kind":"arxiv","version":2},"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:f2a79bc970b45812987bb7678d81be8a8613883f11795aa87f4813e2a0461104","target":"record","created_at":"2026-05-18T02:43:52Z","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":"75e5345a841e68f10cb58500dfecb4306607b6ba41ab04b60a3b9f1d484b53ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T04:35:01Z","title_canon_sha256":"a78a1b67629bcea79852bfdc3d5140835c99dc60a1f81c74bf5a8d5961ae1d59"},"schema_version":"1.0","source":{"id":"1311.3014","kind":"arxiv","version":2}},"canonical_sha256":"ee743b7f8db213044173474bdc70f0375891d8aeb67ff027ee8ec36ccf0a423d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee743b7f8db213044173474bdc70f0375891d8aeb67ff027ee8ec36ccf0a423d","first_computed_at":"2026-05-18T02:43:52.323337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:52.323337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yr06TfoWEgbSQtubpaJhLSs93u5Esl4Iss3Daji5wZONcqr63SD/QumC0+WQBkP+26yVE8bFqlRO1sr6tdJbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:52.323772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3014","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a79bc970b45812987bb7678d81be8a8613883f11795aa87f4813e2a0461104","sha256:f5f94128ce3561552c3eda52a21ad939e43232bc6b85560da429296d7f423cb7"],"state_sha256":"75e68dba080117c65202fab045a51e9b9b60c956993d0c3addb62a642686b83b"}