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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 D. Bowman and D. M. Bradley, J. Comb. Theory, Ser. A 97, 43-61 (2002; Zbl 1021.11026)]. As an application, a new proof of the formula ζ(3,1,3,1,...,3,1)=2π 4n /(4n+2)!, where {3,1} is repeated n times, is given. Some new identities for the multiple zeta function are also obtained.
MSC:
11M41Other Dirichlet series and zeta functions
05A99Classical combinatorial problems
05E99Algebraic combinatorics