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Antisymmetry and enumeration of LL algorithms
Submitted by Joe Miller on Thu, 08/04/2005 - 07:38.
I have been trying to enumerate all LL algorithms, (following Bernard Helmstetter's work) and cannot seem to reduce the 62208 permutations to the 1211 he has come up with. I am unaware of whether or not he used antisymmetry for his reductions. Using GAP and U rotations and reflections I have come up with a total of 8020. Initially considering antisymmetry as well (removing order 2 permutations and the identity from consideration. Note: I did not consider antisymmetric positions with dihedral symmetry or reflections) still does not bring it close to 1211. I was using Martin Schoenert's method in GAP and a very slow algorithm I wrote to determine equivalence classes from conjugation with a group (automorphism) separately with the same results. If anyone would like to see my definitions I will post them.
Also: Does anyone know of a method to employ the inverse homomorphism in GAP on the cube without forcing GAP to consider such a large space (the WHOLE cube space?). Thank you for your time. -Joe |
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