All Questions
4 questions
8
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GAP cannot solve Rubik's cube 4x4x4 and higher ? (Practical limits of Schreier–Sims algorithm)
According to our practical experiments and literature search - computer algebra system GAP cannot "solve" Rubik's cube 4x4x4 and higher. That means cannot decompose given random element of ...
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4
votes
1
answer
251
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Diameter of the "Masterball-puzzle" permutation groups by a kind of Cartier-Foata enumeration?
There is an wonderful blog post by Jordan S. Ellenberg SHOULD YOU BE SURPRISED BY THE DIAMETER OF THE NXNXN RUBIK’S GROUP?. Which explains how one can come to $N^2log(N)$ estimate of the diameter of ...
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1
vote
0
answers
175
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Random walk on N-Rubik cube group is going like sqrt(number of moves) or linear (number of moves) or? "commutative" vs. "free"(like) group pattern?
Consider higher (NxNxN) Rubik's cube group, with specific set of generators described below.
What is important - that there are huge COMMUTING subsets of generators.
Question: Consider a random walk ...
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13
votes
1
answer
2k
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Number of positions of Rubik's cube grows with multiplier 13 with the distance - what are explanations and groups with similar growth pattern?
Rubik's cube and its generalizations attracts certain attention of mathematical community. It is somehow "noteworthy" that it has been proved that diameter of the Rubik's cube group is 20, i.e. ...
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