An exotic shuffle relation for multiple zeta values

Abstract.

In this short note we will provide a new proof of the following exotic shuffle relation of multiple zeta values: This was proved by Zagier when n = 0, by Broadhurst when m = 0, and by Borwein, Bradley, and Broadhurst when m = 1. In general this was proved by Bowman and Bradley. Our new idea is to use the method of Borwein et al. to reduce the above general relation to some families of combinatorial identities which can be verified by Zeilberger’s algorithm [9, 10] that is part of the WZ method.