Quasicrystals: algebraic, combinatorial and geometrical aspects

Abstract

The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the description of their properties we use the methods of combinatorics on words.

19 pages, 3 postscript figures, contribution to the Proceedings of NATO School "Physics and Computer Science", Cargese 2005

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