{"id":"e-4575133542136945","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-490435c99149594f","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_eval_nonpos","RealRooted.threeTerm_interlaces","RealRooted.eval_nonpos_of_natDegree_le_two"],"certificate_hash":"ace38abae4bb16a0b5e34fb620a80630b49b01772f25c6bbdf55e35faa91e444","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":3136,"certificate_compressed_size":1210,"conclusion_name":"Triangle T(n,k) read by rows: coefficient of [x^k] of the polynomial p_n(x)=(5-x)*p_{n-1}(x)-p_{n-2}(x), p_0=1, p_1=5-x.","claims":[{"claim":"real_rooted","from_index":0,"region":{}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-490435c99149594f","claim":"real_rooted"},{"node_id":"n-490435c99149594f","claim":"interlacing"}]}