{"id":"e-7e5628a5a6fa16d5","operation":{"operation":"basis_map_theorem"},"operation_detail":null,"conclusion_id":"n-3cb22164e2f83fe1","premise_count":0,"theorem":"ray basis maps: for L f = (a + b t) f + kappa (t - h) f', b > 0, kappa >= 0, and g real-rooted with every root <= h, of multiplicity m at h, T(u^k) = L^k g sends every real polynomial with all roots in S to one with all roots in (-inf, h] if and only if S lies in (-inf, a + b h + kappa m] (RealRooted rayBasisMap_maps_realRootedIn_iff; the step is Ma and Wang, EJC 15 (2008) R17, Theorem 2)","lean_route":null,"lean_declarations":[],"certificate_hash":"c2d209d08abec6ecd7b37e40fa1124bf9f957a3329f324266d2fb87c15b3a186","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map_theorem","certificate_raw_size":1999,"certificate_compressed_size":843,"conclusion_name":"Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.","claims":[{"claim":"basis_map_preserver","input_interval":"(-inf, 1]","output_interval":"(-inf, 0]","statement":"source (-inf, a + b h + kappa m] = (-inf, 1] with m = 0, target (-inf, 0]"}],"premises":[],"cited_by":[{"node_id":"n-3cb22164e2f83fe1","claim":"basis_map_preserver"}]}