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Cut-and-project graphs and other complexes

Theoretical Computer Science, 2021
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Gregory L McColm
exaly   +2 more sources

A characterisation of linear repetitivity for cut and project sets with general polytopal windows [PDF]

open access: yesIndagationes Mathematicae
The cut and project method is a central construction in the theory of Aperiodic Order for generating quasicrystals with pure point diffraction. Linear repetitivity (LR) is a form of ideal regularity of aperiodic patterns.
James Walton
exaly   +5 more sources

Sharp density discrepancy for cut and project sets an approach via lattice point counting [PDF]

open access: yesMonatshefte Fur Mathematik
Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace. We seek to quantify fluctuations from the asymptotic mean for point counts.
Michael Bjorklund   +2 more
exaly   +6 more sources

Cut-and-project sets and their -duals

Philosophical Magazine, 2007
Motivated by approximation and real analysis, Meyer introduced model sets (also called cut-and-project sets), which are used as mathematical models of quasicrystals. In his study, a central role was played by the ϵ-dual. The ϵ-dual of a lattice is the reciprocal lattice, and that of a cut-and-project set is contained by the diffraction pattern.
Y. Akama, S. Iizuka
openaire   +1 more source

Inflation centres of the cut and project quasicrystals

Journal of Physics A: Mathematical and General, 1998
Cut-and-project quasicrystals which display golden ratio inflation symmetries are investigated. The subclass with convex window is exhaustively described with respect to the possible inflation centres, both internal and external to the point set. Also, the possible inflation factors themselves are determined and found to form a 1D quasicrystal.
Masáková, Zuzana   +2 more
openaire   +2 more sources

Cut-and-project sequences and substitution rules

Ferroelectrics, 2001
Abstract We consider infinite words in a 3-letter alphabet which arise from the cut-and-project scheme based on quadratic unitary Pisot numbers. Such sequences may be considered as ternary generalizations of classical Sturmian sequences. We describe the complexity of such sequences and give a condition under which these generalized Sturmian sequences ...
Zuzana Masáková, Edita Pelantová
openaire   +1 more source

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