{"id":"e-8ff02e4505879db1","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-f239c3b0ba932394","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":"sign","lean_declarations":["RealRooted.threeTerm_interlaces_of_nonnegCoeffs","RealRooted.threeTerm_interlaces","RealRooted.threeTerm_hasNonnegCoeffs"],"certificate_hash":"4a4b4fb2c5cb31be31ce08ba3712b00c81f312eaba961ccef2765c6f1113f9d7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":3878,"certificate_compressed_size":1383,"conclusion_name":"Triangle T(n,k), read by rows, given by (1,-1,0,0,0,0,0,0,0,0,0,...) DELTA (1,0,-1,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-f239c3b0ba932394","claim":"real_rooted"},{"node_id":"n-f239c3b0ba932394","claim":"one_signed_coefficients"},{"node_id":"n-f239c3b0ba932394","claim":"hadamard_kernel"},{"node_id":"n-f239c3b0ba932394","claim":"interlacing"}]}