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 - 2001/12/1

Y1 - 2001/12/1

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

VL - 57

SP - 766

EP - 771

JO - Acta Crystallographica Section B: Structural Science

JF - Acta Crystallographica Section B: Structural Science

SN - 0108-7681

IS - 6

ER -