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University of North Texas

1. Risley, Rebecca N. A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence.

Degree: 1998, University of North Texas

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 V2+ε and, in the Sturmian case, arbitrarily large subwords of the form V3+ε. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental. Advisors/Committee Members: Zamboni, Luca Quardo, 1962-, Jackson, Steve, 1957-, Iaia, Joseph A..

Subjects/Keywords: Arnoux-Rauzy sequences; Sturmian sequences; mathematics; Sequences (Mathematics)

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APA (6th Edition):

Risley, R. N. (1998). A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc278440/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Risley, Rebecca N. “A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence.” 1998. Thesis, University of North Texas. Accessed August 08, 2020. https://digital.library.unt.edu/ark:/67531/metadc278440/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Risley, Rebecca N. “A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence.” 1998. Web. 08 Aug 2020.

Vancouver:

Risley RN. A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence. [Internet] [Thesis]. University of North Texas; 1998. [cited 2020 Aug 08]. Available from: https://digital.library.unt.edu/ark:/67531/metadc278440/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Risley RN. A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence. [Thesis]. University of North Texas; 1998. Available from: https://digital.library.unt.edu/ark:/67531/metadc278440/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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