{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:J2WXTH7XTOZ62SRUVSXQPELCNB","short_pith_number":"pith:J2WXTH7X","schema_version":"1.0","canonical_sha256":"4ead799ff79bb3ed4a34acaf079162684ec1a147ce56d25793a7cabc21596a15","source":{"kind":"arxiv","id":"0907.2870","version":1},"attestation_state":"computed","paper":{"title":"On the least common multiple of $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2009-07-16T15:34:57Z","abstract_excerpt":"In this paper, we prove the following identity $$ \\lcm({n\\brack 0}_q,{n\\brack 1}_q,...,{n\\brack n}_q) =\\frac{\\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)]."},"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":"0907.2870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-07-16T15:34:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"980761b8d4eaaf5dfc938700118d31d85582eb660ea31a589bf3a73df5045067","abstract_canon_sha256":"b8190313d12ce3ac5d341ef3f47a1f2378351c91509ca45d5af845efe4b6dc3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.570876Z","signature_b64":"7Lz9M43kIxv5egXIRBP/qV5ecF2MIReW1JN/8abgOoWYv17/RhalX6li28zQ3KcNfEfg8Aa/ZmSeSnrRRG3IAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ead799ff79bb3ed4a34acaf079162684ec1a147ce56d25793a7cabc21596a15","last_reissued_at":"2026-05-18T04:26:01.570418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.570418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the least common multiple of $q$-binomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2009-07-16T15:34:57Z","abstract_excerpt":"In this paper, we prove the following identity $$ \\lcm({n\\brack 0}_q,{n\\brack 1}_q,...,{n\\brack n}_q) =\\frac{\\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2870","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":"0907.2870","created_at":"2026-05-18T04:26:01.570489+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.2870v1","created_at":"2026-05-18T04:26:01.570489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2870","created_at":"2026-05-18T04:26:01.570489+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2WXTH7XTOZ6","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2WXTH7XTOZ62SRU","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2WXTH7X","created_at":"2026-05-18T12:26:00.592388+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/J2WXTH7XTOZ62SRUVSXQPELCNB","json":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB.json","graph_json":"https://pith.science/api/pith-number/J2WXTH7XTOZ62SRUVSXQPELCNB/graph.json","events_json":"https://pith.science/api/pith-number/J2WXTH7XTOZ62SRUVSXQPELCNB/events.json","paper":"https://pith.science/paper/J2WXTH7X"},"agent_actions":{"view_html":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB","download_json":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB.json","view_paper":"https://pith.science/paper/J2WXTH7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.2870&json=true","fetch_graph":"https://pith.science/api/pith-number/J2WXTH7XTOZ62SRUVSXQPELCNB/graph.json","fetch_events":"https://pith.science/api/pith-number/J2WXTH7XTOZ62SRUVSXQPELCNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB/action/storage_attestation","attest_author":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB/action/author_attestation","sign_citation":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB/action/citation_signature","submit_replication":"https://pith.science/pith/J2WXTH7XTOZ62SRUVSXQPELCNB/action/replication_record"}},"created_at":"2026-05-18T04:26:01.570489+00:00","updated_at":"2026-05-18T04:26:01.570489+00:00"}