{"paper":{"title":"Fractional L-intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Niranjan Balachandran, Rogers Mathew, Tapas Kumar Mishra","submitted_at":"2018-03-11T12:23:41Z","abstract_excerpt":"Let $L = \\{\\frac{a_1}{b_1}, \\ldots , \\frac{a_s}{b_s}\\}$, where for every $i \\in [s]$, $\\frac{a_i}{b_i} \\in [0,1)$ is an irreducible fraction. Let $\\mathcal{F} = \\{A_1, \\ldots , A_m\\}$ be a family of subsets of $[n]$. We say $\\mathcal{F}$ is a \\emph{fractional $L$-intersecting family} if for every distinct $i,j \\in [m]$, there exists an $\\frac{a}{b} \\in L$ such that $|A_i \\cap A_j| \\in \\{ \\frac{a}{b}|A_i|, \\frac{a}{b} |A_j|\\}$. In this paper, we introduce and study the notion of fractional $L$-intersecting families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03954","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"}