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Friedland's Lower Matching Conjecture asserts that if G is a d-regular bipartite graph on v(G) = 2n vertices, and m k (G) denotes the number of matchings of size k, then m k (G) ≥ n k 2 2010 Mathematics Subject Classification. Primary: 05C35. Secondary: 05C31, 05C70, 05C80.doi:10.4171/jems/706 fatcat:v5qut6eyszc4xkqwxihykyiyzy