{"id":"hexagon/2611.00101","pdf":"https://hexagonmath.org/pdf/2611.00101v1","url":"https://hexagonmath.org/abs/2611.00101v1","tags":["math.CO","msc:11B85","msc:11J70","msc:68R15","msc:11T71","Baum-Sweet sequence","Hankel determinants","automatic sequences","continued fractions","linear complexity"],"score":0,"title":"The Hankel determinants of the Baum-Sweet sequence are 2-automatic","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"Let b be the Baum-Sweet sequence and H_n = det(b_{i+j})_{0<=i,j<n} its Hankel determinants over F_2. We prove that the sequence chi_0(n) = [H_n != 0] is 2-automatic: chi_0(n+1) is computed by an explicit automaton with 8 states reading the binary expansion of n, and the minimal automaton of chi_0 reading least significant digits first has 74 states. The same holds for the shifted determinants det(b_{i+j+1}), with the same 8-state graph and 68 states. This contrasts with Mkaouar's theorem that the partial quotients of the Baum-Sweet series are not automatic. On the way we show that Theta = t…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}