Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-29T17:48:02.265Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted Model Sets and their Higher Point-Correlations

Published online by Cambridge University Press:  20 November 2018

Xinghua Deng  and
Robert V. Moody
Xinghua Deng
Affiliation:
Department of Mathematics, Ocean University of China, Qingdao, 266071, China e-mail: xdeng@ouc.edu.cn
Robert V. Moody
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria BC, V8W 3R4 e-mail: rmoody@uvic.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

52C2351P0574E1560G55model setscorrelationsdiffraction

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 487 - 497
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, 9023–9038. 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, 506–541. 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, 621–637. 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, 310–323. 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. 403–441.Google Scholar
[9] Moody, R. V., Uniform distribution in model sets. Canad. Math. Bull. 45(2002), no. 1, 123–130. http://dx.doi.org/10.4153/CMB-2002-015-3 Google Scholar