We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by an underlying periodic structure. We show that every Arnoux-Rauzy sequence contains arbitrarily large subwords of the form V^2+ε and, in the Sturmian case, arbitrarily large subwords of the form V^3+ε. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278440 |
| Date | 08 1900 |
| Creators | Risley, Rebecca N. |
| Contributors | Zamboni, Luca Quardo, 1962-, Jackson, Steve, 1957-, Iaia, Joseph A. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 45 leaves, Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Risley, Rebecca N. |
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