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Weighted Model Sets and their Higher Point-Correlations

Published online by Cambridge University Press:  20 November 2018

Xinghua Deng
Affiliation:
Department of Mathematics, Ocean University of China, Qingdao, 266071, Chinae-mail: [email protected]
Robert V. Moody
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria BC, V8W 3R4e-mail: [email protected]
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Abstract

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Examples of distinct weighted model sets with equal 2, 3, 4, 5-point correlations are given.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Baake, M. and Moody, R. V., Diffractive point sets with entropy. J. Phys. A 31(1998), no. 45, 90239038. http://dx.doi.org/10.1088/0305-4470/31/45/003 Google Scholar
[2] Bourbaki, N., Éléments de mathématique. Groupes et algèbres de Lie. Ch. 4, 5, and 6, Hermann, Paris, 1968.Google Scholar
[3] Deng, X. and Moody, R. V., Dworkin's argument revisited: point processes, dynamics, diffraction, and correlations. J. Geom. Phys. 58(2008), no. 4, 506541. http://dx.doi.org/10.1016/j.geomphys.2007.12.006 Google Scholar
[4] Deng, X. and Moody, R. V., How model sets can be determined by their two-point and three-point correlations. J. Stat. Phys. 135(2009), no. 4, 621637. http://dx.doi.org/10.1007/s10955-009-9742-0 Google Scholar
[5] Gähler, F., Crystallography of dodecagonal quasicrystals. In: Quasicrystalline materials: Proceedings of the I.L.L. / Codest Workshop (Grenoble, 21–25 March 1988), World Scientific, Singapore, 1988.Google Scholar
[6] GrÜnbaum, F. A. and Moore, C. C., The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Acta Cryst. Sect. A 51(1995), no. 3, 310323. http://dx.doi.org/10.1107/S0108767394009827 Google Scholar
[7] Lenz, D. and Moody, R. V., Stationary processes with pure point diffraction. In preparation.Google Scholar
[8] Moody, R. V., Model sets and their duals. In: The mathematics of long-range aperiodic order (Waterloo, ON, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 489, Kluwer, Dordrecht, 1997, pp. 403441.Google Scholar
[9] Moody, R. V., Uniform distribution in model sets. Canad. Math. Bull. 45(2002), no. 1, 123130. http://dx.doi.org/10.4153/CMB-2002-015-3 Google Scholar