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Matrix Representation of Harmonic Sums

Research paper by Lin Jiu

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Combinatorics



Abstract

We provide an alternative computation for harmonic sums through multiplication of matrices, special cases of which are interpreted as stochastic matrices associated to random walks, so that harmonic sums are recognized as probabilities of certain paths. Diagonalization of these matrices allows to recover and generalize a combinatorial identity. General matrix representation of multiplicative nested sums leads to more combinatorial identities.