{"id":"e-29094c360cdb0314","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-22693abd431a71f2","premise_count":0,"theorem":"L. L. Liu and Y. Wang, A unified approach to polynomial sequences with only real zeros, Adv. in Appl. Math. 38 (2007) 542-560, Theorem 2.1 with g = f' (as in their Corollary 2.4), with nonnegativity of the coefficients replaced by an exact induction keeping every root in (-inf, 0)","lean_route":null,"lean_declarations":[],"certificate_hash":"e75d164c2aae4fefc96384f344c3c401f35b229fc75306c971006e12e4d065ef","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":2717,"certificate_compressed_size":1028,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-22693abd431a71f2","claim":"real_rooted"},{"node_id":"n-22693abd431a71f2","claim":"one_signed_coefficients"},{"node_id":"n-22693abd431a71f2","claim":"hadamard_kernel"},{"node_id":"n-22693abd431a71f2","claim":"interlacing"}]}
