{"id":"e-4a8bd3a5d986eb7b","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-2feb6dc01f424b0a","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":"4efa4cf803a8145dfeeae2aa6da95e108ce132363b8c44509ae2068853c79ced","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":2747,"certificate_compressed_size":1038,"conclusion_name":"Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....","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-2feb6dc01f424b0a","claim":"interlacing"},{"node_id":"n-2feb6dc01f424b0a","claim":"real_rooted"},{"node_id":"n-2feb6dc01f424b0a","claim":"one_signed_coefficients"},{"node_id":"n-2feb6dc01f424b0a","claim":"hadamard_kernel"}]}
