The Algebra and Combinatorics of Shuffles and Multiple Zeta Values

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.

21 pages, available online at http://www.idealibrary.com

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• Duality for Finite Multiple Harmonic q-Series
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• Signed q-Analogs of Tornheim's Double Series
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• Braids, Shuffles and Symmetrizers
• Double Shuffle Relations of Euler Sums
• Generalized shuffles related to Nijenhuis and TD-algebras
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• Yamamoto's interpolation of finite multiple zeta and zeta-star values
• Some relations deduced from regularized double shuffle relations of multiple zeta values
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• A note on evaluations of multiple zeta values
• Finite automata and relations of multiple zeta values
• Bowman-Bradley type theorem for finite multiple zeta values in ${\mathcal{A}}_2$
• A note on ${\mathcal{F}}_n$-multiple zeta values