A classification of one dimensional almost periodic tilings arising from the projection method
Author:
James A. Mingo
Journal:
Trans. Amer. Math. Soc. 352 (2000), 52635277
MSC (1991):
Primary 05B45, 52C22, 46L89
Published electronically:
July 18, 2000
MathSciNet review:
1709776
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: For each irrational number , with continued fraction expansion , we classify, up to translation, the one dimensional almost periodic tilings which can be constructed by the projection method starting with a line of slope . The invariant is a sequence of integers in the space and whenever modulo the equivalence relation generated by tail equivalence and . Each tile in a tiling , of slope , is coded by an integer . Using a composition operation, we produce a sequence of tilings . Each tile in gets absorbed into a tile in . A choice of a starting tile in will thus produce a sequence in . This is the invariant.
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Additional Information
James A. Mingo
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
Email:
mingoj@mast.queensu.ca
DOI:
http://dx.doi.org/10.1090/S0002994700026209
PII:
S 00029947(00)026209
Received by editor(s):
August 4, 1998
Received by editor(s) in revised form:
May 1, 1999
Published electronically:
July 18, 2000
Additional Notes:
Research supported by the Natural Sciences and Engineering Research Council of Canada and The Fields Institute for Research in the Mathematical Sciences
Article copyright:
© Copyright 2000
by the author
