On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

Details On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

1996-04-22

arxiv.org/abs/hep-th/9604128v1

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, LaTeX

Scientific paper

A generating function is given for the number, $E(l,k)$, of irreducible $k$-fold Euler sums, with all possible alternations of sign, and exponents summing to $l$. Its form is remarkably simple: $\sum_n E(k+2n,k) x^n = \sum_{d|k}\mu(d) (1-x^d)^{-k/d}/k$, where $\mu$ is the M\"obius function. Equivalently, the size of the search space in which $k$-fold Euler sums of level $l$ are reducible to rational linear combinations of irreducible basis terms is $S(l,k) = \sum_{n

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