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

Richard M. Thompson, Robert T Downs

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)766-771
Number of pages6
JournalActa Crystallographica Section B: Structural Science
Volume57
Issue number6
DOIs
StatePublished - Dec 2001

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Group theory
group theory
Labels
equivalence
Equivalence classes
coding
Binary trees
symmetry

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.

In: Acta Crystallographica Section B: Structural Science, Vol. 57, No. 6, 12.2001, p. 766-771.

Research output: Contribution to journalArticle

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