{"paper":{"title":"A symmetrical q-Eulerian identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guoniu Han, Jiang Zeng, Zhicong Lin","submitted_at":"2012-01-24T10:28:00Z","abstract_excerpt":"We find a $q$-analog of the following symmetrical identity involving binomial coefficients $\\binom{n}{m}$ and Eulerian numbers $A_{n,m}$, due to Chung, Graham and Knuth [{\\it J. Comb.}, {\\bf 1} (2010), 29--38]: {equation*} \\sum_{k\\geq 0}\\binom{a+b}{k}A_{k,a-1}=\\sum_{k\\geq 0}\\binom{a+b}{k}A_{k,b-1}. {equation*} We give two proofs, using generating function and bijections, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4941","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"}