{"paper":{"title":"Generalizations of Joints Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Yang","submitted_at":"2016-06-28T00:52:32Z","abstract_excerpt":"We generalize the joints problem to sets of varieties and prove almost sharp bound on the number of joints. As a special case, given a set of $N$ $2$-planes in $\\mathbb{R}^6$, the number of points at which three $2$-planes intersect and span $\\mathbb{R}^6$ is at most $CN^{3/2+\\epsilon}$. We also get almost sharp bound on the number of joints with multiplicities. The main tools are polynomial partitioning and induction on dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08525","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"}