Arnoux-Rauzy Subshifts: Linear Recurrence, Powers, and Palindromes

Details Arnoux-Rauzy Subshifts: Linear Recurrence, Powers, and Palindromes Arnoux-Rauzy Subshifts: Linear Recurrence, Powers, and Palindromes

2002-08-19

arxiv.org/abs/math/0208137v1

Mathematics

Combinatorics

17 pages

Scientific paper

We consider Arnoux-Rauzy subshifts $X$ and study various combinatorial questions: When is $X$ linearly recurrent? What is the maximal power occurring in $X$? What is the number of palindromes of a given length occurring in $X$? We present applications of our combinatorial results to the spectral theory of discrete one-dimensional Schr\"odinger operators with potentials given by Arnoux-Rauzy sequences.

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