{"id":"e-d4161fce9e8d4a19","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-948c4fae35fcbf15","premise_count":1,"theorem":"Veronese sections of Polya frequency sequences (Aissen--Schoenberg--Whitney--Edrei): if P is real-rooted with coefficients of one sign, equivalently nonzero with all roots in (-inf, 0], every section V_(r,j)(P) is zero or real-rooted with roots in (-inf, 0]","lean_route":null,"lean_declarations":[],"certificate_hash":"8020016517a2cba4c631061573bfc51ee2a0c4e383ea2648bfafe8ba0a030f76","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8706,"certificate_compressed_size":2326,"conclusion_name":"veronese_section_2_0 of Triangle read by rows: T(n, k) = binomial(2n, 2k).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[{"position":0,"node_id":"n-f7935c36a3c0ec8c","role":"sequence","name":"Triangle read by rows: T(n, k) = binomial(2n, 2k).","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-948c4fae35fcbf15","claim":"real_rooted"},{"node_id":"n-948c4fae35fcbf15","claim":"one_signed_coefficients"},{"node_id":"n-948c4fae35fcbf15","claim":"hadamard_kernel"},{"node_id":"n-948c4fae35fcbf15","claim":"interlacing"}]}