{"id":"e-f1b8ea4179e62f14","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-579c11d996f64808","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":"e70d652cdb7c43bac70021001d70181b99ac58d500cacc3ec97e0efbdf8366bc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":9063,"certificate_compressed_size":2438,"conclusion_name":"veronese_section_2_0 of Triangle read by rows: T(n,k) = binomial(k,n-k).","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-21854f4257effb01","role":"sequence","name":"Triangle read by rows: T(n,k) = binomial(k,n-k).","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-579c11d996f64808","claim":"real_rooted"},{"node_id":"n-579c11d996f64808","claim":"one_signed_coefficients"},{"node_id":"n-579c11d996f64808","claim":"hadamard_kernel"},{"node_id":"n-579c11d996f64808","claim":"interlacing"}]}