{"id":"e-7d811e606f00941d","operation":{"map":"A013610","operation":"basis_map"},"operation_detail":"A013610","conclusion_id":"n-fb83cf6de9ce04de","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":"05f0fd70691ec9faa3d0678b99a6876f3e182423e7619f4813f12702c3823fc1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14286,"certificate_compressed_size":2684,"conclusion_name":"basis_map_A013610 of Triangle of Dyck paths counted by number of long interior inclines.","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-c963abfc0266d66c","role":"sequence","name":"Triangle of Dyck paths counted by number of long interior inclines.","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-fb83cf6de9ce04de","claim":"real_rooted"},{"node_id":"n-fb83cf6de9ce04de","claim":"one_signed_coefficients"},{"node_id":"n-fb83cf6de9ce04de","claim":"hadamard_kernel"},{"node_id":"n-fb83cf6de9ce04de","claim":"interlacing"}]}