{"id":"e-5274dd88a300ad29","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-d300994ed88c0a37","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":"9235cfdeb72eba1a179530af0d61e8446b121d78fb86f1e9851bf754fefd6010","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13759,"certificate_compressed_size":2613,"conclusion_name":"basis_map_A013611 of Coefficients of a special case of Poisson-Charlier polynomials.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-c9dce8c25621fdea","role":"sequence","name":"Coefficients of a special case of Poisson-Charlier polynomials.","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-d300994ed88c0a37","claim":"real_rooted"},{"node_id":"n-d300994ed88c0a37","claim":"one_signed_coefficients"},{"node_id":"n-d300994ed88c0a37","claim":"hadamard_kernel"},{"node_id":"n-d300994ed88c0a37","claim":"interlacing"}]}