Open AccessVoronoi Cells of Beta-Integers
Author(s) -
Avi Elkharrat,
Christiane Frougny
Publication year - 2005
Publication title -
lecture notes in computer science
Language(s) - English
Resource type - Book series
SCImago Journal Rank - 0.249
H-Index - 400
eISSN - 1611-3349
pISSN - 0302-9743
ISBN - 3-540-26546-5
DOI - 10.1007/11505877_19
Subject(s) - voronoi diagram , combinatorics , mathematics , beta (programming language) , symmetry (geometry) , quadratic equation , word (group theory) , computer science , geometry , programming language
In this paper are considered one-dimensional tilings arising from some Pisot numbers encountered in quasicrystallography as the quadratic Pisot units and the cubic Pisot unit associated with 7-fold symmetry, and also the Tribonacci number. We give characterizations of the Voronoi cells of such tilings, using word combinatorics and substitutions.
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