{"id":"e-6eebb6934276f7fa","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-4ad294e2bfbb52a6","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.threeTerm_interlaces_of_window"],"certificate_hash":"629b99b54c67703c799a5a9059d6b79f4c8f6afee9cea484a8853c128b29fe58","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":4577,"certificate_compressed_size":1498,"conclusion_name":"Triangle read by rows: T(n,k) is the number of 2-compositions of n having length k (0 <= k <= n).","claims":[{"claim":"real_rooted","from_index":0,"region":{"lower":{"closed":true,"value":"-1"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-4ad294e2bfbb52a6","claim":"real_rooted"},{"node_id":"n-4ad294e2bfbb52a6","claim":"interlacing"}]}