{"paper":{"title":"Arithmetic Properties of Overpartition Triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang","submitted_at":"2014-10-29T08:27:49Z","abstract_excerpt":"Let ${{\\overline{p}}_{3}}(n)$ be the number of overpartition triples of $n$. By elementary series manipulations, we establish some congruences for ${\\overline{p}}_{3}(n)$ modulo small powers of 2, such as\n  \\[{{\\overline{p}}_{3}}(16n+14)\\equiv 0 \\pmod{32}, \\quad {{\\overline{p}}_{3}}(8n+7)\\equiv 0 \\pmod{64}.\\] We also find many arithmetic properties for ${{\\overline{p}}_{3}}(n)$ modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers $\\alpha \\ge 1$ and $n \\ge 0$, we have ${{\\overline{p}}_{3}}\\big({{3}^{2\\alpha +1}}(3n+2)\\big)\\equiv 0$ (mod $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7898","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"}