{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:W5TLNKGFLYKHVNID5YX34XO35Z","short_pith_number":"pith:W5TLNKGF","schema_version":"1.0","canonical_sha256":"b766b6a8c55e147ab503ee2fbe5ddbee5487f335842c111195f1cf42e6562b05","source":{"kind":"arxiv","id":"1403.5327","version":1},"attestation_state":"computed","paper":{"title":"Kronecker Coefficients For Some Near-Rectangular Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vasu V. Tewari","submitted_at":"2014-03-21T00:18:49Z","abstract_excerpt":"We give formulae for computing Kronecker coefficients occurring in the expansion of $s_{\\mu}*s_{\\nu}$, where both $\\mu$ and $\\nu$ are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study $s_{(n,n-1,1)}*s_{(n,n)}$, $s_{(n-1,n-1,1)}*s_{(n,n-1)}$, $s_{(n-1,n-1,2)}*s_{(n,n)}$, $s_{(n-1,n-1,1,1)}*s_{(n,n)}$ and $s_{(n,n,1)}*s_{(n,n,1)}$. Our approach relies on the interplay between manipulation of symmetric functions and the representation theory of the symmetric group, mainly employing the Pieri rule and a useful identity of Littlewood. As a consequence of th"},"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":"1403.5327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-21T00:18:49Z","cross_cats_sorted":[],"title_canon_sha256":"94a31e31aae4caf7a3711a66ea8714a9acf804dcbfda0f471deb4d4df39189ba","abstract_canon_sha256":"dd013648fa1c38651854784d0f16dc6474a3f8bef34f020fa58b026bea68fee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:56.679448Z","signature_b64":"UuogH0eRpCLU6YNuUkw2WbarFOSHeWLxBsrLlWWqLOFt5kOXpcIKxO3+rZ2r60YJWEN/OE6pTUCCWMVV9h8mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b766b6a8c55e147ab503ee2fbe5ddbee5487f335842c111195f1cf42e6562b05","last_reissued_at":"2026-05-18T02:55:56.678906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:56.678906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kronecker Coefficients For Some Near-Rectangular Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vasu V. Tewari","submitted_at":"2014-03-21T00:18:49Z","abstract_excerpt":"We give formulae for computing Kronecker coefficients occurring in the expansion of $s_{\\mu}*s_{\\nu}$, where both $\\mu$ and $\\nu$ are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study $s_{(n,n-1,1)}*s_{(n,n)}$, $s_{(n-1,n-1,1)}*s_{(n,n-1)}$, $s_{(n-1,n-1,2)}*s_{(n,n)}$, $s_{(n-1,n-1,1,1)}*s_{(n,n)}$ and $s_{(n,n,1)}*s_{(n,n,1)}$. Our approach relies on the interplay between manipulation of symmetric functions and the representation theory of the symmetric group, mainly employing the Pieri rule and a useful identity of Littlewood. As a consequence of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5327","kind":"arxiv","version":1},"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":"1403.5327","created_at":"2026-05-18T02:55:56.678991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5327v1","created_at":"2026-05-18T02:55:56.678991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5327","created_at":"2026-05-18T02:55:56.678991+00:00"},{"alias_kind":"pith_short_12","alias_value":"W5TLNKGFLYKH","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"W5TLNKGFLYKHVNID","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"W5TLNKGF","created_at":"2026-05-18T12:28:54.890064+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/W5TLNKGFLYKHVNID5YX34XO35Z","json":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z.json","graph_json":"https://pith.science/api/pith-number/W5TLNKGFLYKHVNID5YX34XO35Z/graph.json","events_json":"https://pith.science/api/pith-number/W5TLNKGFLYKHVNID5YX34XO35Z/events.json","paper":"https://pith.science/paper/W5TLNKGF"},"agent_actions":{"view_html":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z","download_json":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z.json","view_paper":"https://pith.science/paper/W5TLNKGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5327&json=true","fetch_graph":"https://pith.science/api/pith-number/W5TLNKGFLYKHVNID5YX34XO35Z/graph.json","fetch_events":"https://pith.science/api/pith-number/W5TLNKGFLYKHVNID5YX34XO35Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z/action/storage_attestation","attest_author":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z/action/author_attestation","sign_citation":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z/action/citation_signature","submit_replication":"https://pith.science/pith/W5TLNKGFLYKHVNID5YX34XO35Z/action/replication_record"}},"created_at":"2026-05-18T02:55:56.678991+00:00","updated_at":"2026-05-18T02:55:56.678991+00:00"}