{"id":"e-031a48225080e193","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-9116f92e53f934a9","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"66ee81c0c8fa7be1713102d4c913d6f20690f5e5e0aa4e5454965cfef0eb7ea3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10294,"certificate_compressed_size":2288,"conclusion_name":"basis_map_A013609 of Triangle of central factorial numbers |t(2n,2n-2k)| read by rows.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-e734a631f8279507","role":"sequence","name":"Triangle of central factorial numbers |t(2n,2n-2k)| read by rows.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-9116f92e53f934a9","claim":"one_signed_coefficients"},{"node_id":"n-9116f92e53f934a9","claim":"hadamard_kernel"},{"node_id":"n-9116f92e53f934a9","claim":"interlacing"},{"node_id":"n-9116f92e53f934a9","claim":"real_rooted"}]}