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Some multi-set inclusions associated with shuffle convolutions and multiple zeta values. (English) Zbl 1016.11035
The authors develop a new method for obtaining combinatorial identities involving shuffle convolutions [see {\it D. Bowman} and {\it D. M. Bradley}, J. Comb. Theory, Ser. A 97, 43-61 (2002; Zbl 1021.11026)]. As an application, a new proof of the formula $\zeta (3,1,3,1,\ldots ,3,1)=2\pi^{4n}/(4n+2)!$, where $\{ 3,1\}$ is repeated $n$ times, is given. Some new identities for the multiple zeta function are also obtained.

MSC:
 11M41 Other Dirichlet series and zeta functions 05A99 Classical combinatorial problems 05E99 Algebraic combinatorics
Full Text:
References:
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