{"id":"e-8c219f5be19a6675","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-4acec5e35bbb846a","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":"926f158281c0b51fb8b9fe980eb27c6893c43c23cd73d3e7b4818f38e29ef368","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14131,"certificate_compressed_size":2649,"conclusion_name":"basis_map_A013611 of Delannoy paths counted by number of weak peaks.","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-b31aa1a3fd93d174","role":"sequence","name":"Delannoy paths counted by number of weak peaks.","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-4acec5e35bbb846a","claim":"real_rooted"},{"node_id":"n-4acec5e35bbb846a","claim":"one_signed_coefficients"},{"node_id":"n-4acec5e35bbb846a","claim":"hadamard_kernel"},{"node_id":"n-4acec5e35bbb846a","claim":"interlacing"}]}