{"paper":{"title":"Regularly spaced subsums of integer partitions","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla D. Savage, E. Rodney Canfield, Herbert S. Wilf","submitted_at":"2003-08-07T01:56:12Z","abstract_excerpt":"For integer partitions $\\lambda :n=a_1+...+a_k$, where $a_1\\ge a_2\\ge >...\\ge a_k\\ge 1$, we study the sum $a_1+a_3+...$ of the parts of odd index. We show that the average of this sum, over all partitions $\\lambda$ of $n$, is of the form $n/2+(\\sqrt{6}/(8\\pi))\\sqrt{n}\\log{n}+c_{2,1}\\sqrt{n}+O(\\log{n}).$ More generally, we study the sum $a_i+a_{m+i}+a_{2m+i}+...$ of the parts whose indices lie in a given arithmetic progression and we show that the average of this sum, over all partitions of $n$, is of the form $n/m+b_{m,i}\\sqrt{n}\\log{n}+c_{m,i}\\sqrt{n}+O(\\log{n})$, with explicitly given consta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308061","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"}