{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VC3FA2K5EKEBJZX3Q6GDS6P3GP","short_pith_number":"pith:VC3FA2K5","schema_version":"1.0","canonical_sha256":"a8b650695d228814e6fb878c3979fb33e8121a192d74f5eb191d73a8eae4c7c6","source":{"kind":"arxiv","id":"1204.2484","version":2},"attestation_state":"computed","paper":{"title":"Deciding Positivity of Littlewood-Richardson Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Christian Ikenmeyer, Peter B\\\"urgisser","submitted_at":"2012-04-11T16:01:35Z","abstract_excerpt":"Starting with Knutson and Tao's hive model (in J. Amer. Math. Soc., 1999) we characterize the Littlewood-Richardson coefficient $c_{\\lambda,\\mu}^\\nu$ of given partitions $\\lambda,\\mu,\\nu\\in N^n$ as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding $c_{\\lambda,\\mu}^\\nu >0$. This algorithm is easy to state and takes $O(n^3 \\log \\nu_1)$ arithmetic operations and comparisons. We further show that the capacity achieving hive flows can be seen as the vertices of a connected graph, which leads to new structural insigh"},"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":"1204.2484","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-11T16:01:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7223ca9b15394eba40a68151f3b92bbd34e754ee4123b4da638642e4bfa8aecd","abstract_canon_sha256":"2226902523060bf1f0e36bc5229bc038bd0bd633a05fe6c7589e65ab18ac7553"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:23.400699Z","signature_b64":"FZG283nlRN9UDEMnW+J209JwRNVOFIWy9mjNZQlJvix901qCm0vYw3ySp1eZZzm1iC1l7Ii6v6uG/saofM6cAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8b650695d228814e6fb878c3979fb33e8121a192d74f5eb191d73a8eae4c7c6","last_reissued_at":"2026-05-18T03:19:23.400137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:23.400137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deciding Positivity of Littlewood-Richardson Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Christian Ikenmeyer, Peter B\\\"urgisser","submitted_at":"2012-04-11T16:01:35Z","abstract_excerpt":"Starting with Knutson and Tao's hive model (in J. Amer. Math. Soc., 1999) we characterize the Littlewood-Richardson coefficient $c_{\\lambda,\\mu}^\\nu$ of given partitions $\\lambda,\\mu,\\nu\\in N^n$ as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding $c_{\\lambda,\\mu}^\\nu >0$. This algorithm is easy to state and takes $O(n^3 \\log \\nu_1)$ arithmetic operations and comparisons. We further show that the capacity achieving hive flows can be seen as the vertices of a connected graph, which leads to new structural insigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2484","kind":"arxiv","version":2},"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":"1204.2484","created_at":"2026-05-18T03:19:23.400226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2484v2","created_at":"2026-05-18T03:19:23.400226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2484","created_at":"2026-05-18T03:19:23.400226+00:00"},{"alias_kind":"pith_short_12","alias_value":"VC3FA2K5EKEB","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VC3FA2K5EKEBJZX3","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VC3FA2K5","created_at":"2026-05-18T12:27:25.539911+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/VC3FA2K5EKEBJZX3Q6GDS6P3GP","json":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP.json","graph_json":"https://pith.science/api/pith-number/VC3FA2K5EKEBJZX3Q6GDS6P3GP/graph.json","events_json":"https://pith.science/api/pith-number/VC3FA2K5EKEBJZX3Q6GDS6P3GP/events.json","paper":"https://pith.science/paper/VC3FA2K5"},"agent_actions":{"view_html":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP","download_json":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP.json","view_paper":"https://pith.science/paper/VC3FA2K5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2484&json=true","fetch_graph":"https://pith.science/api/pith-number/VC3FA2K5EKEBJZX3Q6GDS6P3GP/graph.json","fetch_events":"https://pith.science/api/pith-number/VC3FA2K5EKEBJZX3Q6GDS6P3GP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP/action/storage_attestation","attest_author":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP/action/author_attestation","sign_citation":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP/action/citation_signature","submit_replication":"https://pith.science/pith/VC3FA2K5EKEBJZX3Q6GDS6P3GP/action/replication_record"}},"created_at":"2026-05-18T03:19:23.400226+00:00","updated_at":"2026-05-18T03:19:23.400226+00:00"}