{"id":"e-80d7320f7911dda9","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-367366cbd49283c0","premise_count":2,"theorem":"Hermite--Kakeya--Obreschkoff: real-rooted f, g with interlacing zeros give a zero or real-rooted a f + b g for all real a, b (Obreschkoff 1963; Fisk, Polynomials, roots, and interlacing, Thm 1.43)","lean_route":null,"lean_declarations":[],"certificate_hash":"59fc96a6c16a39bf84f91c2f4109ad011f364e3c3f380443acee24dab406d2b2","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":12152,"certificate_compressed_size":2687,"conclusion_name":"obreschkoff_combination of Triangle read by rows, the Bell transform of the quartic factorial numbers A007696(n+1) without column 0.","claims":[{"claim":"real_rooted","from_index":1,"region":{}}],"premises":[{"position":0,"node_id":"n-5c56442adc0376c2","role":"sequence","name":"Triangle read by rows, the Bell transform of the quartic factorial numbers A007696(n+1) without column 0.","uses":{"claim":"real_rooted","from_index":1,"region":{}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-5c56442adc0376c2","role":"sequence","name":"Triangle read by rows, the Bell transform of the quartic factorial numbers A007696(n+1) without column 0.","uses":{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 2"}],"cited_by":[{"node_id":"n-367366cbd49283c0","claim":"real_rooted"}]}