{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RJKK2KFAODW23YO2DTE6SJ3K75","short_pith_number":"pith:RJKK2KFA","schema_version":"1.0","canonical_sha256":"8a54ad28a070edade1da1cc9e9276aff54691c57cd724905f2058d4394d7fcd8","source":{"kind":"arxiv","id":"1410.7087","version":3},"attestation_state":"computed","paper":{"title":"Bounds on Kronecker and $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Greta Panova, Igor Pak","submitted_at":"2014-10-26T21:29:12Z","abstract_excerpt":"We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial coefficients $\\binom{n}{k}_q$ as polynomials in~$q$ to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bounds for a wider class of Kronecker coefficients."},"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":"1410.7087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-26T21:29:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f5b7f37d9b6ace36a2dc85f1777c4918e088793f01ea7816732c38ea290c49ba","abstract_canon_sha256":"6124751a196c6d6ab615e0e8f149afbcb5901cf44c144d90780a632b58eff7a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.279855Z","signature_b64":"jgl0fkae4Jn7cPCSVfjJXybS0123INUGnEQVgmtPb6QNMwUsdrjnlkr6OTHHeq3Y8J1f1L6uf9vl5Tm1LlSEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a54ad28a070edade1da1cc9e9276aff54691c57cd724905f2058d4394d7fcd8","last_reissued_at":"2026-05-18T01:15:53.279372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.279372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on Kronecker and $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Greta Panova, Igor Pak","submitted_at":"2014-10-26T21:29:12Z","abstract_excerpt":"We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial coefficients $\\binom{n}{k}_q$ as polynomials in~$q$ to derive sharp bounds on the differences of their consecutive coefficients. We then derive effective asymptotic lower bounds for a wider class of Kronecker coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7087","kind":"arxiv","version":3},"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":"1410.7087","created_at":"2026-05-18T01:15:53.279446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7087v3","created_at":"2026-05-18T01:15:53.279446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7087","created_at":"2026-05-18T01:15:53.279446+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJKK2KFAODW2","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJKK2KFAODW23YO2","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJKK2KFA","created_at":"2026-05-18T12:28:46.137349+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/RJKK2KFAODW23YO2DTE6SJ3K75","json":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75.json","graph_json":"https://pith.science/api/pith-number/RJKK2KFAODW23YO2DTE6SJ3K75/graph.json","events_json":"https://pith.science/api/pith-number/RJKK2KFAODW23YO2DTE6SJ3K75/events.json","paper":"https://pith.science/paper/RJKK2KFA"},"agent_actions":{"view_html":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75","download_json":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75.json","view_paper":"https://pith.science/paper/RJKK2KFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7087&json=true","fetch_graph":"https://pith.science/api/pith-number/RJKK2KFAODW23YO2DTE6SJ3K75/graph.json","fetch_events":"https://pith.science/api/pith-number/RJKK2KFAODW23YO2DTE6SJ3K75/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75/action/storage_attestation","attest_author":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75/action/author_attestation","sign_citation":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75/action/citation_signature","submit_replication":"https://pith.science/pith/RJKK2KFAODW23YO2DTE6SJ3K75/action/replication_record"}},"created_at":"2026-05-18T01:15:53.279446+00:00","updated_at":"2026-05-18T01:15:53.279446+00:00"}