Thurs Jan Feb 10
* go over homework:
- solid cube group in detail (see solid_cube.txt)
** permutation cycles
- group operation of successive permutations
- practice
- cycles
- what "generates" the permutations?
* transpositions
* 3-cycles
** conjugate pairs, U = F R F'
- a notion of "same kind of thing"
- conjugate => same cycle length
and 'same general properties'
** permutation puzzles in general:
- Cayley graph (generator as "lines" leading out from solved to new positions)
- each position is group element of transformation from solved to that position.
- decomposition of each position into permutation cycles
** discuss how to start thinking about "solving" a permutation puzzle
- operators
** Rubik's Cube as a permutation puzzle
- corners
- edges
- faces
** counting positions