@**article**{RISC2381,author = {J.M. Borwein and D.M. Bradley and D.J. Broadhurst and P. Lisonek},

title = {{Combinatorial aspects of multiple zeta values}},

language = {english},

abstract = {Multiple zeta values (MZVs, also called Euler sums or multiple harmonic
series) are nested generalizations of the classical Riemann zeta function
evaluated at integer values. The fact that an integral representation
of MZVs obeys a shuffle product rule allows the possibility
of a combinatorial approach to them. Using this approach we prove
a longstanding conjecture of Don Zagier about MZVs with certain repeated
arguments. We also prove a similar cyclic sum identity. Finally,
we present extensive computational evidence supporting an infinite family
of conjectured MZV identities that simultaneously generalize
the Zagier identity.},

journal = {Electron. J. Combin.},

volume = {5},

pages = {1--12},

isbn_issn = {ISSN 1077-8926},

year = {1998},

refereed = {yes},

length = {12}

}