A classification of one dimensional almost periodic tilings arising from the projection method

Author:
James A. Mingo

Journal:
Trans. Amer. Math. Soc. **352** (2000), 5263-5277

MSC (1991):
Primary 05B45, 52C22, 46L89

DOI:
https://doi.org/10.1090/S0002-9947-00-02620-9

Published electronically:
July 18, 2000

MathSciNet review:
1709776

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-00-02620-9

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