Classification of one-dimensional quasilattices into mutual local-derivability classes

Details Classification of one-dimensional quasilattices into mutual local-derivability classes Classification of one-dimensional quasilattices into mutual local-derivability classes

2000-09-27

arxiv.org/abs/cond-mat/0009422v4

J. Phys. Soc. Jpn. vol.71, 99-118 (2002)

Physics

Condensed Matter

Materials Science

42 pages, latex, 5 eps figures, Published in JPSJ

Scientific paper

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.

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