{"id":"e-c9b6865dc767aa74","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-19f0864da52d8a44","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":"5baee6939094afa2923b715b87238e4540ea1eb624a686c7051c4250f0209858","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8955,"certificate_compressed_size":2422,"conclusion_name":"veronese_section_2_1 of Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.","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-811c78acf96cbc19","role":"sequence","name":"Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.","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-19f0864da52d8a44","claim":"interlacing"},{"node_id":"n-19f0864da52d8a44","claim":"real_rooted"},{"node_id":"n-19f0864da52d8a44","claim":"one_signed_coefficients"},{"node_id":"n-19f0864da52d8a44","claim":"hadamard_kernel"}]}