{"paper":{"title":"Incidence bounds on multijoints and generic joints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marina Iliopoulou","submitted_at":"2014-08-25T19:09:34Z","abstract_excerpt":"A point $x \\in \\mathbb{F}^n$ is a joint formed by a finite collection $\\mathfrak{L}$ of lines in $\\mathbb{F}^n$ if there exist at least $n$ lines in $\\mathfrak{L}$ through $x$ that span $\\mathbb{F}^n$. It is known that there are $\\lesssim_n |\\mathfrak{L}|^{\\frac{n}{n-1}}$ joints formed by $\\mathfrak{L}$.\n  We say that a point $x \\in \\mathbb{F}^n$ is a multijoint formed by the finite collections $\\mathfrak{L}_1,\\ldots,\\mathfrak{L}_n$ of lines in $\\mathbb{F}^n$ if there exist at least $n$ lines through $x$, one from each collection, spanning $\\mathbb{F}^n$. We show that there are $\\lesssim_n (|\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5867","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"}