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An edge $S$ of $H$ is said to represent {\\em fairly} (resp. {\\em almost fairly}) a partition $(V_1,V_2, \\ldots, V_m)$ of $V(H)$ if $|S\\cap V_i|\\ge \\lfloor\\frac{|V_i|}{\\beta(H)}\\rfloor$ (resp. $|S\\cap V_i|\\ge \\lfloor\\frac{|V_i|}{\\beta(H)}\\rfloor-1$) for all $i \\le m$.\n  In matroids any partition of $V(H)$ can be represented fairly by some independent set. We look for classes of hypergraphs $H$ in which any partition of $V(H)$ can be represented almost fairly by some edge.\n  We show that this is true"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.03196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-10T06:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"6c35f3f6561febb8b16a716cd63c5ea638ed95d5f64af021eaf5dea130f17a53","abstract_canon_sha256":"e093826d0ac750c8a9ce983e9243208ffd096991eb7bea17e8ab5cc096cb4690"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:41.054407Z","signature_b64":"o3bwyd37p8AobPYvIMByCAJvwsEE5KGlGaxLjjaIUz1BxH8aBFTqZC4nMqLJG/k7ym/36+yAgmKJB/H05DMPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a4f378055d1629caf2b7ccf2ac860909e585ab7989fe98764c8b16f7d166a6d","last_reissued_at":"2026-05-18T00:59:41.053670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:41.053670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fair representation by independent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dani Kotlar, Eli Berger, Maria Chudnovsky, Martin Loebl, Noga Alon, Ran Ziv, Ron Aharoni","submitted_at":"2016-11-10T06:31:33Z","abstract_excerpt":"For a hypergraph $H$ let $\\beta(H)$ denote the minimal number of edges from $H$ covering $V(H)$. 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