- #1

Anko

- 32

- 3

I'm going over some old uni notes, and I'm hoping to learn a bit more about categories and things like fibrations.

But in 3rd year, we looked at the Klein 4-group. I know of two examples, one where I can have an additive V

_{4}acting on pairs of two-way crossbar switches, in what I suppose is the Benes construction or switching net.

The other is when it acts on a 4-tuple of vertices, in the rotation subgroup of D

_{4}if I give each vertex of the square an index from {00, 01, 10, 11} then I add 1 to the appropriate row or column index, four at a time. So V

_{4}is in both places as a free additive group, which I need to restrict?

The thing I'm getting at I think is, what does any restriction on V

_{4}then have to do with an inductive kind of algorithm, particularly in the Benes construction, where the other half of the exercise is to route inputs to outputs, without blocking. Thus a switching algorithm is a requirement.