Speed-optimal algs for centers

[DrKorbin]

X-centers
T-centers - TBD

Notes:
1) My buffer for X-centers is Ubr.
2) [A, B] = A B A' B'
3) S [A, B] = S A B A' B' S' (yes, I'm aware of notation [S : [A, B]], this is just shorter).
4) Check out for cancelations.
z' L' [d, l' U l] = z' L' d l' U l d' l' U' Lw z
U' [Uw r Uw', l'] = u r Uw' l' Uw r' Uw' l U
5) Almost all algs are move optimal (if you consider U, Uw, u, U2, Uw2, u2 as 1 move). However, sometimes I use almost optimal algs to avoid cube rotations.
6) If you find a better alg, please write it here.

PS: Any good algs for Ubr > Ufl > Dfr and Ubr > Ufl > Dbl?

 

[Ollie]

Excellent

 

[NevinsCPH]

Amazing! Hoping to see T centers.

 

[tim]

PS: Any good algs for Ubr > Ufl > Dfr and Ubr > Ufl > Dbl?

I came here for exactly these two cases. Left disappointed.
Jokes aside: Thanks for the list! I already discovered a few cases I execute awkwardly.

 

[DrKorbin]

I came here for exactly these two cases. Left disappointed.

Well, you can do a setup to Ubr > Ufl > Dfl, and there will be 13 moves total. But maybe there is a better alg?

 

[A Leman]

This is awesome! I use the Ubr buffer and thought I would have to make my own list since almost everyone uses UBL for corners. Thank you so much.

For the 2 cycles you listed, they are Per-specials for corners and since the 12 mover is terrible I would do a D/D' setup to the coloumns case l Ur2U l' U'r2U lU2l'. For corners I rotate perspecials to [R'UR:RU'R',D2] but I only just realized that works on centers as r'ur2u'r' D2 rur' D2 r'u'r. I think the second one is much worse for centers than corners with all of the slice turns.

 

[Ollie]

y2 x' (r) U r2 U (l') U' r2 U (l) U2 (r') x y2

 

[Christopher Mowla]

To the OP, I'm not sure if most of your commutators are considered speed optimal by a lot of speedcubers.

Here are some commutators in better move sets.
[Rw U' l' U, r] (10)
[r U' r' U r', F] (12)

You can get different cases from each by shifting each algorithm as well as systematically inverting different groups of moves within each algorithm. (And of course, you can also conjugate as you do the other two things just mentioned).

 

[DrKorbin]

To the OP, I'm not sure if most of your commutators are considered speed optimal by a lot of speedcubers.

Here are some commutators in better move sets.
[Rw U' l' U, r] (10)
[r U' r' U r', F] (12)

Ummm, what?

[Rw U' l' U, r] does Ful > Fur > Dfr.
[r U' r' U r', F] does Ubr > Frd > Fru.
I don't always make a threecycle with both stickers of F, but when I do it, I do a pure comm (8 moves).