{"paper":{"title":"Proof of a conjecture of Mircea Merca","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":"2014-05-19T14:49:15Z","abstract_excerpt":"We prove that, for any prime $p$ and positive integer $r$ with $p^r>2$, the number of multinomial coefficients such that $$ {k\\choose k_1,k_2,\\ldots,k_n}=p^r,\\quad \\text{and}\\quad k_1+2k_2+\\cdots+nk_n=n, $$ is given by $$ \\delta_{p^r,\\,k}\\left(\\left\\lfloor\\frac{n-1}{p^r-1}\\right\\rfloor -\\delta_{0,\\,n\\bmod p^r} \\right), $$ where $\\delta_{i,j}$ is the Kronecker delta and $\\lfloor x\\rfloor$ stands for the largest integer not exceeding $x$. This confirms a recent conjecture of Mircea Merca."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4755","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"}