{"paper":{"title":"Fair representation in the intersection of two matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar, Eli Berger, Ran Ziv, Ron Aharoni","submitted_at":"2016-12-22T15:39:44Z","abstract_excerpt":"For a simplicial complex ${\\mathcal C}$ denote by $\\beta({\\mathcal C})$ the minimal number of edges from ${\\mathcal C}$ needed to cover the ground set. If ${\\mathcal C}$ is a matroid then for every partition $A_1, \\ldots, A_m$ of the ground set there exists a set $S \\in {\\mathcal C}$ meeting each $A_i$ in at least $\\frac{|A_i|}{\\beta({\\mathcal C})}$ elements. We conjecture that a slightly weaker result is true for the intersections of two matroids: if ${\\mathcal D}={\\mathcal P} \\cap {\\mathcal Q}$, where ${\\mathcal P},{\\mathcal Q}$ are matroids on the same ground set $V$ and $\\beta({\\mathcal P}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07652","kind":"arxiv","version":3},"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"}