The singlet contribution to the Bjorken sum rule for polarized deep inelastic scattering

It is shown that the existing four-loop result for the Bjorken polarized sum rule for deep inelastic electron-nucleon scattering obtained within perturbative Quantum Chromodynamics should be supplemented by the calculation of the diagrams of the so called singlet type. We also give an explanation of the interesting coincidence of two different classes of diagrams, one of the non-singlet and one of the singlet type, contributing the $\alpha_s^4$-approximation to the total cross-section of electron-positron annihilation into hadrons.