Return to search

A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence

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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc278440
Date08 1900
CreatorsRisley, Rebecca N.
ContributorsZamboni, Luca Quardo, 1962-, Jackson, Steve, 1957-, Iaia, Joseph A.
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatiii, 45 leaves, Text
RightsPublic, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Risley, Rebecca N.

Page generated in 0.0017 seconds