{"id":"e-e6a18deaef81a66e","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-72cbbb2f152c8f9c","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction","lean_route":null,"lean_declarations":["RealRooted.MaWang.strictInterl_of_interlaces_evalCoeff_nonpos"],"certificate_hash":"69b9129f3cd354d1ed9fbe42485ebfa9e0ff3a387ff670a30f7875c9373daf74","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4558,"certificate_compressed_size":1265,"conclusion_name":"Triangle T(n,k), read by rows, given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"-1"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-72cbbb2f152c8f9c","claim":"real_rooted"},{"node_id":"n-72cbbb2f152c8f9c","claim":"one_signed_coefficients"},{"node_id":"n-72cbbb2f152c8f9c","claim":"hadamard_kernel"},{"node_id":"n-72cbbb2f152c8f9c","claim":"interlacing"}]}