{"paper":{"title":"Extension of Stanley's Theorem for Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"cs.DM","authors_text":"Manosij Ghosh Dastidar, Sourav Sen Gupta","submitted_at":"2010-07-20T16:21:40Z","abstract_excerpt":"In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between \"the sum of the numbers of distinct members in the partitions of a positive integer $n$\" and \"the total number of 1's that occur in the partitions of $n$\". Our generalization states a similar relation between \"the sum of the numbers of distinct members in the partitions of $n$\" and the total number of 2's or 3's or any general $k$ that occur in the partitions of $n$ and the subsequent integers. We also apply this result to obtain an array of interes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3459","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"}