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Dec
20
revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
added 220 characters in body; added 254 characters in body
Dec
20
comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
@Gerhard Paseman Do you think those cube states are random samples of all possible cube states, or somehow biased?
Dec
20
revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
added 43 characters in body
Dec
20
comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
@Francois Brunault Well, I'm allowing rotations of the face, so 4^3 = 64 states are possible once we fix one face, but you're absolutely right. What I'm trying to understand is, what is the probability that the solved cube is one of those states? Or are those states more or less a random sample of all possible cube states?
Dec
20
comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
@Brendan McKay Version (1) is what I had in mind. I don't want to condition on the cells being in the correct positions for a solved cube.
Dec
20
awarded  Commentator
Dec
20
comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
@Francois Brunault I'm looking to make a statement of just how frequently you can solve the cube when you fix one or more faces. The answer, no doubt, will be "very infrequently".
Dec
20
comment Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
@Greg Martin :)
Dec
20
revised Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
deleted 6 characters in body; edited title
Dec
20
asked Counting the number of Rubik's cube states in which k = 0 to 4 of the faces are “solved”
Dec
5
revised Manhattan distance vs. absorption time on an unbounded integer lattice
added 257 characters in body
Dec
5
revised Manhattan distance vs. absorption time on an unbounded integer lattice
Incorrectly placed decimal position for percentage values.
Dec
5
revised Manhattan distance vs. absorption time on an unbounded integer lattice
deleted 99 characters in body
Dec
5
comment Manhattan distance vs. absorption time on an unbounded integer lattice
@Alexandre Eremenko Right, I'm having some trouble understanding how this problem works in the continuum limit, so I keep talking about Manhattan distances instead of Euclidean distances (where I'm not sure why it makes sense to talk about them on a lattice). Small $L$ means $L \leq 100$ or so.
Dec
4
revised Manhattan distance vs. absorption time on an unbounded integer lattice
Added a data point at (0, 0, 30) for walker initialization; added 17 characters in body
Dec
4
revised Manhattan distance vs. absorption time on an unbounded integer lattice
added 1460 characters in body
Dec
4
revised Manhattan distance vs. absorption time on an unbounded integer lattice
added 324 characters in body; added 42 characters in body