{"paper":{"title":"Higgledy-piggledy subspaces and uniform subspace designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"P\\'eter Sziklai, Szabolcs L. Fancsali","submitted_at":"2014-09-22T16:09:46Z","abstract_excerpt":"In this article, we investigate collections of `well-spread-out' projective (and linear) subspaces. Projective $k$-subspaces in $\\mathsf{PG}(d,\\mathbb{F})$ are in `higgledy-piggledy arrangement' if they meet each projective subspace of co-dimension $k$ in a generator set of points. We prove that the set $\\mathcal{H}$ of higgledy-piggledy $k$-subspaces has to contain more than $\\min{|\\mathbb{F}|,\\sum_{i=0}^k\\lfloor\\frac{d-k+i}{i+1}\\rfloor}$ elements. We also prove that $\\mathcal{H}$ has to contain more than $(k+1)\\cdot(d-k)$ elements if the field $\\mathbb{F}$ is algebraically closed.\n  An $r$-u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6227","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"}