{"id":"e-e835bed38a18a979","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-3f0a1785078e99be","premise_count":0,"theorem":"L. L. Liu and Y. Wang, A unified approach to polynomial sequences with only real zeros, Adv. in Appl. Math. 38 (2007) 542-560, Theorem 2.1 with g = f' (as in their Corollary 2.4), with nonnegativity of the coefficients replaced by an exact induction keeping every root in (-inf, 0)","lean_route":null,"lean_declarations":[],"certificate_hash":"5646780afafafb3b15ba64c0d7eeb32f0af3a8ebaedeb85301ad443c39448273","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":3298,"certificate_compressed_size":1133,"conclusion_name":"Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 2*x + 5.","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-3f0a1785078e99be","claim":"real_rooted"},{"node_id":"n-3f0a1785078e99be","claim":"one_signed_coefficients"},{"node_id":"n-3f0a1785078e99be","claim":"hadamard_kernel"},{"node_id":"n-3f0a1785078e99be","claim":"interlacing"}]}
