{"id":"e-6814b23dac2e2745","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-ced86a7ce48c966e","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":"b45c8f22d22eee923c22d3d14e687ec6609db78e7772fbcd5cfe19c3b9a35910","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":6197,"certificate_compressed_size":1673,"conclusion_name":"Triangle read by rows: T(n,k) is the number of circular binary words of length n having k occurrences of 01 (0 <= k <= floor(n/2)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-ced86a7ce48c966e","claim":"real_rooted"},{"node_id":"n-ced86a7ce48c966e","claim":"one_signed_coefficients"},{"node_id":"n-ced86a7ce48c966e","claim":"hadamard_kernel"},{"node_id":"n-ced86a7ce48c966e","claim":"interlacing"}]}
