The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class rather than on their value. These quantities express the anomalous dimensions and Wilson coefficients in massless QED and QCD. We show how to find a basis of the associated algebra and present counting relations for the different index classes. Two further classes of relations are discussed.
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