{"id":"e-7519e7535554cb98","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-28595a60eb57b37f","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":"a7c1fa4b4ac6e2186843feeee5d68990bc77661ce6c7d1e0cb2907ee9b6b5eb9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":3293,"certificate_compressed_size":1117,"conclusion_name":"Triangle of B-analogs of Stirling numbers of 2nd kind.","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-28595a60eb57b37f","claim":"real_rooted"},{"node_id":"n-28595a60eb57b37f","claim":"one_signed_coefficients"},{"node_id":"n-28595a60eb57b37f","claim":"hadamard_kernel"},{"node_id":"n-28595a60eb57b37f","claim":"interlacing"}]}
