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2012 PISOT DUAL TILINGS OF LOW DEGREE AND THEIR DISCONNECTEDNESS
Nertila Gjini
Author Affiliations +
Albanian J. Math. 6(1): 21-32 (2012). DOI: 10.51286/albjm/1346250294

Abstract

We study the connectedness of the graph-directed self-affine tiles associated to β−expansions, called Pisot dual tilings. These tiles are examples of Rauzy fractals and play an important role in the study of β-expansion, substitution and symbolic dynamical system. Using the complete classification of the β-expansion of 1 for quartic Pisot units and the classification of the connected tilings given in [4] and [5], here we continue studying connectedness of Pisot dual tilings generated by a Pisot unit with integral minimal equation x4ax3bx2cx1=0 in the special case when a+c2β. It is shown that every tile is disconnected having infinitely many connected components.

Citation

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Nertila Gjini. "PISOT DUAL TILINGS OF LOW DEGREE AND THEIR DISCONNECTEDNESS." Albanian J. Math. 6 (1) 21 - 32, 2012. https://doi.org/10.51286/albjm/1346250294

Information

Published: 2012
First available in Project Euclid: 13 July 2023

Digital Object Identifier: 10.51286/albjm/1346250294

Subjects:
Primary: 68P30 , 81P70 , 94A10

Keywords: connectedness , Dual Tiling , greedy expansion , Rauzy Fractal

Rights: Copyright © 2012 Research Institute of Science and Technology (RISAT)

Vol.6 • No. 1 • 2012
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