{"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"}