{"paper":{"title":"Multifactorisations and Divisor Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ambrose D. Law, Karl Michael Schmidt, Matthew C. Lettington","submitted_at":"2023-03-21T17:27:53Z","abstract_excerpt":"We consider a joint ordered multifactorisation for a given positive integer $n\\geq 2$ into $m$ parts, where $n=n_1~\\times~\\ldots~\\times~n_m$, and each part $n_j$ is split into one or more component factors. Our central result gives an enumeration formula for all such joint ordered multifactorisations $\\mathcal{N}_m(n)$. As an illustrative application, we show how each such factorisation can be used to uniquely construct and so count the number of distinct additive set systems (historically referred to as complementing set systems). These set systems under set addition generate the first $n$ no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12042","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.12042/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}