{"paper":{"title":"Incidences between points and lines in R^4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Micha Sharir, Noam Solomon","submitted_at":"2014-11-04T03:47:53Z","abstract_excerpt":"We show that the number of incidences between $m$ distinct points and $n$ distinct lines in ${\\mathbb R}^4$ is $O\\left(2^{c\\sqrt{\\log m}} (m^{2/5}n^{4/5}+m) + m^{1/2}n^{1/2}q^{1/4} + m^{2/3}n^{1/3}s^{1/3} + n\\right)$, for a suitable absolute constant $c$, provided that no 2-plane contains more than $s$ input lines, and no hyperplane or quadric contains more than $q$ lines. The bound holds without the factor $2^{c\\sqrt{\\log m}}$ when $m \\le n^{6/7}$ or $m \\ge n^{5/3}$. Except for this factor, the bound is tight in the worst case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0777","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"}