2002/09/19 by Johannes Kellendonk, Mark V. Lawson, Kellendonk, Johannes +2
Engineering · Materials Science · Mathematics · Physics and Astronomy · #20M18 #52C23 #Commutative Algebra (math.AC) #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Mathematics and Applications #Quasicrystal Structures and Properties #graph theory and CDMA systems #math-ph #math.AC #math.GR #math.MP #msc:20M18 #msc:52C23
paper · pdf · doi:10.48550/arxiv.math/0209250
24 pages
arxiv created 2002/09/19 · openalex publication_date 2002/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of point sets which are obtained by a cut and projection scheme (so-called model sets). Here we introduce another inverse semigroup which is given in terms of the defining data of the projection scheme and related to the model set by the empire congruence. The second class is given by one-dimensional tilings.