{"id":"e-6ddcf5c6f38774e7","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-954f0c79bf5b2ac0","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":"c8694901a5e1ee741bc89ad0a4b8be8ee6c3815dcf5790116fa2864f6678eab3","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":5921,"certificate_compressed_size":1603,"conclusion_name":"obreschkoff_combination of Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 2.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-880485a065802fcb","role":"sequence","name":"Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 2.","uses":{"claim":"real_rooted","from_index":0,"region":{}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-880485a065802fcb","role":"sequence","name":"Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 2.","uses":{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1"}],"cited_by":[{"node_id":"n-954f0c79bf5b2ac0","claim":"real_rooted"}]}