{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6LMYACTF77W4GJTEKMAGR7OSVS","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":"055c91d84b908915bc8627c8043907c0dae80bf8d4c33d59ab7734fe8c9d14ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-03T21:40:17Z","title_canon_sha256":"e7fd6299027ce99711b3596297a8bcc51bbdf6cca5e1a19c4e9671d35ff62a65"},"schema_version":"1.0","source":{"id":"1403.0607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0607","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0607v1","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0607","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"6LMYACTF77W4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6LMYACTF77W4GJTE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6LMYACTF","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:7eafbcd02d359222a640c8b4b5dd75444cefcf757127a57198fce4f0565cd820","target":"graph","created_at":"2026-05-18T02:57:16Z","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":"We prove a Murnaghan-Nakayama rule for the noncommutative Schur functions introduced by Bessenrodt, Luoto and van Willigenburg. In other words, we give an explicit combinatorial formula for expanding the product of a noncommutative power sum symmetric function and a noncommutative Schur function in terms of noncommutative Schur functions. In direct analogy to the classical Murnaghan-Nakayama rule, the summands are computed using a noncommutative analogue of border strips, and have coefficients equal to 1 or -1 determined by the height of these border strips. The rule is proved by interpreting ","authors_text":"Vasu V. Tewari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-03T21:40:17Z","title":"A Murnaghan-Nakayama Rule For Noncommutative Schur Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0607","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":"sha256:97e41ed511ec327694469eaf7f94fa532e6a284caca9bc88316208c7b6e2f198","target":"record","created_at":"2026-05-18T02:57:16Z","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":"055c91d84b908915bc8627c8043907c0dae80bf8d4c33d59ab7734fe8c9d14ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-03T21:40:17Z","title_canon_sha256":"e7fd6299027ce99711b3596297a8bcc51bbdf6cca5e1a19c4e9671d35ff62a65"},"schema_version":"1.0","source":{"id":"1403.0607","kind":"arxiv","version":1}},"canonical_sha256":"f2d9800a65ffedc32664530068fdd2ac9f7f6dffeb430c9ef6298332b836e308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d9800a65ffedc32664530068fdd2ac9f7f6dffeb430c9ef6298332b836e308","first_computed_at":"2026-05-18T02:57:16.143023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:16.143023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UoZiK27V5XqaA882IFP6eOZbk0V7J7Mf9rzDbXv9pGZl2fwLUze/zFJF9p6U5an9yX7c7XL0BWSmtSpr1v6PDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:16.143645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97e41ed511ec327694469eaf7f94fa532e6a284caca9bc88316208c7b6e2f198","sha256:7eafbcd02d359222a640c8b4b5dd75444cefcf757127a57198fce4f0565cd820"],"state_sha256":"726db2303775cfdb406146bcb44982964263c75c2f378ca3e7621bc39f9b6948"}