Asymptotic orbits of primitive substitutions

Authors:
Marcy Barge;Beverly Diamond;Charles Holton
Affiliations:
Department of Mathematics, Montana State University, Bozeman, MT;Department of Mathematics, College of Charleston, Charleston, SC;Department of Mathematics, University of California, Berkeley, CA
Venue:
Theoretical Computer Science
Year:
2003

Citing 3
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Abstract

A primitive, aperiodic substitution on d letters has at most d2 asymptotic orbits; this bound is sharp. Since asymptotic arc components in tiling spaces associated with substitutions are in 1-1 correspondence with asymptotic words, this provides a bound for those as well.