The algebra and combinatorics of shuffles and multiple zeta values

Authors:
Douglas Bowman;David M. Bradley
Affiliations:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois;Department of Mathematics and Statistics, University of Maine, Orono, Maine
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

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Abstract

The algebraic and combinatorial theory of shuffles, introduced by Chen and Ree, is further developed and applied to the study of multiple zeta values. In particular, we establish evaluations for certain sums of cyclically generated multiple zeta values. The boundary case of our result reduces to a former conjecture of Zagier.