{"id":"e-4266cbd95404e739","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-737bf0cfa519ec4d","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":"bb24ecd17bee31c7ec84d7a16959d1b23ef97f2c0e95395ec9b4e696511283b7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4470,"certificate_compressed_size":1277,"conclusion_name":"veronese_section_2_1 of Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ba3bb18490b15e2e","role":"sequence","name":"Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}.","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-737bf0cfa519ec4d","claim":"real_rooted"},{"node_id":"n-737bf0cfa519ec4d","claim":"one_signed_coefficients"},{"node_id":"n-737bf0cfa519ec4d","claim":"hadamard_kernel"}]}