Acta Crystallographica Section B

Structural Science

Volume 57, Part 6 (December 2001)

research papers

Acta Cryst. (2001). B57, 766-771 [ doi:10.1107/S010876810101552X ]

Systematic generation of all nonequivalent closest-packed stacking sequences of length N using group theory

R. M. Thompson and R. T. Downs

Abstract: An algorithm has been developed that generates all of the nonequivalent closest-packed stacking sequences of length N. There are 2^N + 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 [asymptotically equal to] D_N × S₃, to sort these into crystallographic equivalence classes. This problem is shown to be a constrained version of the classic three-colored necklace problem.

Keywords: closest-packed stacking sequences; group theory.