### 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 ≃ D_{N} × S_{3}, to sort these into crystallographic equivalence classes. This problem is shown to be a constrained version of the classic three-colored necklace problem.

Original language | English (US) |
---|---|

Pages (from-to) | 766-771 |

Number of pages | 6 |

Journal | Acta Crystallographica Section B: Structural Science |

Volume | 57 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2001 |

### Fingerprint

### ASJC Scopus subject areas

- Structural Biology
- Condensed Matter Physics

### Cite this

**Systematic generation of all nonequivalent closest-packed stacking sequences of length N using group theory.** / Thompson, Richard M.; Downs, Robert T.

Research output: Contribution to journal › Article

*Acta Crystallographica Section B: Structural Science*, vol. 57, no. 6, pp. 766-771. https://doi.org/10.1107/S010876810101552X

}

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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UR - http://www.scopus.com/inward/citedby.url?scp=0037898234&partnerID=8YFLogxK

U2 - 10.1107/S010876810101552X

DO - 10.1107/S010876810101552X

M3 - Article

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 -