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THE TILING SEMIGROUPS OF ONE-DIMENSIONAL PERIODIC TILINGS

Part of: Designs and configurations Semigroups

Published online by Cambridge University Press:  23 July 2009

E. R. DOMBI  and
N. D. GILBERT
E. R. DOMBI
Affiliation:
School of Mathematical & Computer Sciences, and The Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK (email: edombi@gmail.com)
N. D. GILBERT*
Affiliation:
School of Mathematical & Computer Sciences, and The Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK (email: n.d.gilbert@hw.ac.uk)
*
✉For correspondence; e-mail: n.d.gilbert@hw.ac.uk
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Abstract

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A one-dimensional tiling is a bi-infinite string on a finite alphabet, and its tiling semigroup is an inverse semigroup whose elements are marked finite substrings of the tiling. We characterize the structure of these semigroups in the periodic case, in which the tiling is obtained by repetition of a fixed primitive word.

Keywords

tilinginverse semigrouppartition

MSC classification

Secondary: 20M18: Inverse semigroups 05B45: Tessellation and tiling problems 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 153 - 160
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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