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

1996/04/22 by David Broadhurst, Broadhurst, D. J. · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.hep-th/9604128

openalex publication_date 1996/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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: ∑_n E(k+2n,k) xⁿ = ∑_d|kμ(d) (1-x^d)^-k/d/k, where μ is the Möbius 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) = ∑_n

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