{"paper":{"title":"Constant Sum Partition of $\\{1,2,...,n\\}$ Into Subsets With Prescribed Orders","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sajidha P, V. Vilfred Kamalappan","submitted_at":"2023-11-30T07:52:29Z","abstract_excerpt":"Studies on partition of $I_n$ = $\\{1, 2, . . . , n\\}$ into subsets $S_1, S_2, . . . , S_x$ so far considered with prescribed sum of the elements in each subset. In this paper, we study constant sum partitions $\\{S_1,S_2,...,S_x\\}$ of $I_n$ with prescribed $|S_i|$, $1 \\leq i \\leq x$. Theorem \\ref{thm 2.3} is the main result which gives a necessary and sufficient condition for a partition set $\\{S_1,S_2,\\ldots, S_x\\}$ of $I_n$ with prescribed $|S_i|$ to be a constant sum partition of $I_n$, $1 \\leq i \\leq x$ and $n > x \\geq 2$. We state its applications in graph theory and also define {\\em const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00089","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.00089/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"}