TY - JOUR
T1 - Systematic generation of all nonequivalent closest-packed stacking sequences of length N using group theory
AU - Thompson, Richard M.
AU - Downs, Robert T.
PY - 2001/12
Y1 - 2001/12
N2 - An algorithm has been developed that generates all of the nonequivalent closest-packed stacking sequences of length N. There are 2N + 2(-1)N different labels for closest-packed stacking sequences of length N using the standard A, B, C notation. These labels are generated using an ordered binary tree. As different labels can describe identical structures, we have derived a generalized symmetry group. Q ≃ DN × S3, to sort these into crystallographic equivalence classes. This problem is shown to be a constrained version of the classic three-colored necklace problem.
AB - An algorithm has been developed that generates all of the nonequivalent closest-packed stacking sequences of length N. There are 2N + 2(-1)N different labels for closest-packed stacking sequences of length N using the standard A, B, C notation. These labels are generated using an ordered binary tree. As different labels can describe identical structures, we have derived a generalized symmetry group. Q ≃ DN × S3, to sort these into crystallographic equivalence classes. This problem is shown to be a constrained version of the classic three-colored necklace problem.
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U2 - 10.1107/S010876810101552X
DO - 10.1107/S010876810101552X
M3 - Article
C2 - 11717475
AN - SCOPUS:0037898234
SN - 0108-7681
VL - 57
SP - 766
EP - 771
JO - Acta Crystallographica Section B: Structural Science
JF - Acta Crystallographica Section B: Structural Science
IS - 6
ER -