{"paper":{"title":"On the maximal weight of $(p,q)$-ary chain partitions with bounded parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.NT","authors_text":"Fabrice Philippe, Filippo Disanto, Laurent Imbert","submitted_at":"2012-12-18T14:46:29Z","abstract_excerpt":"A $(p,q)$-ary chain is a special type of chain partition of integers with parts of the form $p^aq^b$ for some fixed integers $p$ and $q$. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound $m$. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of $m$, asymptotically independent of $\\max(p,q)$, and we provide an efficient algorithm to compute it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4370","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"}