{"paper":{"title":"Counting multijoints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA"],"primary_cat":"math.CO","authors_text":"Marina Iliopoulou","submitted_at":"2014-01-24T16:23:41Z","abstract_excerpt":"Let $\\mathfrak{L}_1$, $\\mathfrak{L}_2$, $\\mathfrak{L}_3$ be finite collections of $L_1$, $L_2$, $L_3$, respectively, lines in $\\mathbb{R}^3$, and $J(\\mathfrak{L}_1, \\mathfrak{L}_2,\\mathfrak{L}_3)$ the set of multijoints formed by them, i.e. the set of points $x \\in \\mathbb{R}^3$, each of which lies in at least one line $l_i \\in \\mathfrak{L}_i$, for all $i=1,2,3$, such that the directions of $l_1$, $l_2$ and $l_3$ span $\\mathbb{R}^3$. We prove here that $|J(\\mathfrak{L}_1, \\mathfrak{L}_2,\\mathfrak{L}_3)|\\lesssim (L_1L_2L_3)^{1/2}$, and we extend our results to multijoints formed by real algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6392","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"}