{"id":"e-582e2f23d54a43e5","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-e7e87c6a9f61cef2","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":"467e9fe0a8bb933e9b2882aad73ad154eea83644561ebb518c5e3c4a4421726a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":10615,"certificate_compressed_size":2852,"conclusion_name":"veronese_section_2_0 of Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, n >= 1.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[{"position":0,"node_id":"n-f24dc5f77f658331","role":"sequence","name":"Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, n >= 1.","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-e7e87c6a9f61cef2","claim":"real_rooted"},{"node_id":"n-e7e87c6a9f61cef2","claim":"one_signed_coefficients"},{"node_id":"n-e7e87c6a9f61cef2","claim":"hadamard_kernel"},{"node_id":"n-e7e87c6a9f61cef2","claim":"interlacing"}]}