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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}"},"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":"1612.07652","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-22T15:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"0cb20650c55ef3edc71f3644db1b50557fd2ce051b14ebda0d24145a4a23b250","abstract_canon_sha256":"4ea9c6a5feb742d84fed1902baf8a1b07ea0b7050dc896847389e4c2cac2fd06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:20.407201Z","signature_b64":"ggXTP5uKHJe/2y2OYDoaKpygLSoKJ6XBM3taz3H962xEN2bkUH7PJicWFgvCp9rGFWTD6XJ2jVgEQw+35tOABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff9af1b761fe10c363f56e2404562929bf406e197f392099b7b8ef83f08594e3","last_reissued_at":"2026-05-18T00:53:20.406786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:20.406786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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