{"id":"e-25619dd96a48ab0e","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-e646c30d067149e7","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"],"certificate_hash":"ba4226e4f08c59585b53158ec942c67e00a985ab8e8c2db3c524439b04d9c5ee","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4023,"certificate_compressed_size":1367,"conclusion_name":"Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments.","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-e646c30d067149e7","claim":"one_signed_coefficients"},{"node_id":"n-e646c30d067149e7","claim":"hadamard_kernel"},{"node_id":"n-e646c30d067149e7","claim":"interlacing"},{"node_id":"n-e646c30d067149e7","claim":"real_rooted"}]}