{"paper":{"title":"A Note on the Manickam-Mikl\\'os-Singhi Conjecture for Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ferdinand Ihringer","submitted_at":"2014-05-05T14:26:31Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over a finite field $\\mathbb{F}_q$. Define a real-valued weight function on the $1$-dimensional vector spaces of $V$ such that the sum of all weights is zero. Let the weight of a subspace $S$ be the sum of the weights of the $1$-dimensional subspaces contained in $S$. In 1988 Manickam and Singhi conjectured that if $n \\geq 4k$, then the number of $k$-dimensional subspaces with nonnegative weight is at least the number of $k$-dimensional subspaces on a fixed $1$-dimensional subspace.\n  Recently, Chowdhury, Huang, Sarkis, Shahriari, and Sudakov proved t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0909","kind":"arxiv","version":3},"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"}