Shuffle-exchange networks have received a great deal of attention as interconnecting networks for parallel computing. One unsolved problem is the minimum number of stages required by a shuffle-exchange network with 2n inputs and outputs to be rearrangeable. It turns out that this problem was studied much earlier by Benes in his work on switching networks. Benes also conjectured that 2n-1 stages suffice for rearrangeability and published the conjecture in a more general setting in 1975. So far, the conjecture has been verified only for n•3. It is felt that the conjecture is a difficult mathematical problem and its solution may require a greater participation of the mathematical community. This note gives a mathematical abstraction of the conjectured devoid of any network connection. It also shows that no number of stages is large enough to guarantee a nonblocking network.
