{"paper":{"title":"A q-analogue of some binomial coefficient identities of Y. Sun","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan-Mei Yang, Victor J. W. Guo","submitted_at":"2010-08-09T09:01:45Z","abstract_excerpt":"We give a $q$-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20] as follows: {align*} \\sum_{k=0}^{\\lfloor n/2\\rfloor}{m+k\\brack k}_{q^2}{m+1\\brack n-2k}_{q} q^{n-2k\\choose 2} &={m+n\\brack n}_{q}, \\sum_{k=0}^{\\lfloor n/4\\rfloor}{m+k\\brack k}_{q^4}{m+1\\brack n-4k}_{q} q^{n-4k\\choose 2} &=\\sum_{k=0}^{\\lfloor n/2\\rfloor}(-1)^k{m+k\\brack k}_{q^2}{m+n-2k\\brack n-2k}_{q}, {align*} where ${n\\brack k}_q$ stands for the $q$-binomial coefficient. We provide two proofs, one of which is combinatorial via partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1469","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"}