{"paper":{"title":"Partitions and the maximal excludant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shane Chern","submitted_at":"2019-05-15T17:25:52Z","abstract_excerpt":"For each nonempty integer partition $\\pi$, we define the maximal excludant of $\\pi$ to be the largest nonnegative integer smaller than the largest part of $\\pi$ that is not a part of $\\pi$. Let $\\sigma\\!\\operatorname{maex}(n)$ be the sum of maximal excludants over all partitions of $n$. We show that the generating function of $\\sigma\\!\\operatorname{maex}(n)$ is closely related to a mock theta function studied by Andrews \\textit{et al.} and Cohen. Further, we show that, as $n\\to \\infty$, $\\sigma\\!\\operatorname{maex}(n)$ is asymptotic to the sum of largest parts of all partitions of $n$. Finally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06304","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"}