{"paper":{"title":"Arithmetic Properties of Partition Triples With Odd Parts Distinct","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang","submitted_at":"2014-07-21T09:35:12Z","abstract_excerpt":"Let $\\mathrm{pod}_{-3}(n)$ denote the number of partition triples of $n$ where the odd parts in each partition are distinct. We find many arithmetic properties of $\\mathrm{pod}_{-3}(n)$ involving the following infinite family of congruences: for any integers $\\alpha \\ge 1$ and $n\\ge 0$, \\[\\mathrm{pod}_{-3}\\Big({{3}^{2\\alpha +2}}n+\\frac{23\\times {{3}^{2\\alpha +1}}+3}{8}\\Big)\\equiv 0 \\pmod{9}.\\] We also establish some arithmetic relations between $\\mathrm{pod}(n)$ and $\\mathrm{pod}_{-3}(n)$, as well as some congruences for $\\mathrm{pod}_{-3}(n)$ modulo 7 and 11."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5433","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"}