The Hopf algebra structure of multiple harmonic sums
نویسنده
چکیده
LiI(x1, . . . , xn) = AI(∞;x1, . . . , xk) are called multiple polylogarithms [2]: they generalize the classical polylogarithm Lin(x1) = A(n)(∞;x1). It is immediate from the defining equations (1) and (2) that the sums SI can be written in terms of the AI . To state the relation precisely, let C(n) be the set of compositions of n, i.e., ordered sequences (i1, . . . , ik) of positive integers with i1 + · · · + ik = n. If I = (i1, . . . , ik) is a composition of n and J = (j1, . . . , jp) is a composition of k, then there is a composition J ◦ I of n given by
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