arXiv:2605.09489. Resolves Knuth's TAOCP Pre-Fascicle 8a, Exercise 7.2.2.4–224: the shift-and-save-or-bump digraph
SB(3, n) admits no Hamiltonian cycle for even n. A sign-of-permutation obstruction — writing the successor map as f
S = A
b ∘ σ and computing sgn via a dihedral Burnside argument — gives the stronger statement that
SB(m, n) has no Hamiltonian cycle whenever m is odd, m ≡ 3 (mod 4), and n is even. Included in
TAOCP Pre-Fascicle 8A.