Normal PLL (Permutation of the Last Layer) contains only even permutations. However, in certain puzzles (for instance, the Square-1 and the 4x4x4) this restriction is absent because of the existence of parity. This means that on these puzzles we can get a PLL that is not one of the normal 21 found on the 3x3x3 - that is, we can get a Parity PLL.
The following page gives a list of all the parity PLLs, along with some tentative names. Unlike normal PLL, there is no official/traditional naming scheme, probably because few people have bothered to learn algorithms for each of these cases. These cases can simply be solved by doing a parity algorithm and then solving the normal PLL case, but it may be faster to have a one-look alg for them, depending on the puzzle.
- Upload parity PLL images (why isn't this working) - Add images, names, 4x4 algs (on separate page?), sq1 algs (on separate page?) - Link with other pages