{"id":"e-85a39184a92c1cf8","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-e7331b0d50084c15","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":"36338aab848af192c891e87d3d363121490cd0f4162d76313a281b74df300116","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4021,"certificate_compressed_size":1368,"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-e7331b0d50084c15","claim":"real_rooted"},{"node_id":"n-e7331b0d50084c15","claim":"one_signed_coefficients"},{"node_id":"n-e7331b0d50084c15","claim":"hadamard_kernel"},{"node_id":"n-e7331b0d50084c15","claim":"interlacing"}]}