The Hankel determinants of the Baum-Sweet sequence are 2-automatic
Source: hexagonmath.org/abs/2611.00101v1
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…
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