In this dissertation we solve two fundamental, and until now only partially treated, problems associated with multi-step solution approaches for the Rubik's Cube: the average effect of partial commutativity and cancellation of moves at the step interfaces, and the minimization with respect to certain group-theoretic constraints the number of required move sequences comprising the step look-up tables. The results may be adapted to other permutation groups to some extent, although portions of this work depend explicitly on the interplay between the geometry of the hexahedron and the structure of the Rubik's Cube group.
|Commitee:||Davidson, Morley, Farrell, Paul, Gagola, Stephen, Reynolds, Anne, Yu, Gang|
|School:||Kent State University|
|School Location:||United States -- Ohio|
|Source:||DAI-B 78/11(E), Dissertation Abstracts International|
|Keywords:||Cancellation, Combinatorial group theory, Count, Cube, Move-count, Rubik, Rubik's cube, Word|
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