{"paper":{"title":"Mean Divisibility of Multinomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shigeki Akiyama","submitted_at":"2012-12-16T03:57:23Z","abstract_excerpt":"Let m_1,...,m_s be positive integers. Consider the sequence defined by multinomial coefficients: a_n=\\binom{(m_1+m_2+... +m_s)n}{m_1 n, m_2 n,..., m_s n}. Fix a positive integer k\\ge 2. We show that there exists a positive integer C(k) such that \\frac{\\prod_{n=1}^t a_{kn}}{\\prod_{n=1}^t a_n} \\in \\frac 1{C(k)} \\Z for all positive integer t, if and only if GCD(m_1,...,m_s)=1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3750","kind":"arxiv","version":3},"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"}