Introduction to algorithms
Some combinatorial properties of Sturmian words
Theoretical Computer Science
Palindromes in the Fibonacci word
Information Processing Letters
Sturmian words, Lyndon words and trees
Theoretical Computer Science
The exact number of squares in Fibonacci words
Theoretical Computer Science
Concrete Math
The Number of Irreducible Polynomials and Lyndon Words with Given Trace
SIAM Journal on Discrete Mathematics
Many to One Embeddings from Grids into Cylinders, Tori, and Hypercubes
SIAM Journal on Computing
The distance geometry of music
Computational Geometry: Theory and Applications
Hi-index | 5.23 |
A string p = p0p1...pn-1 of non-negative integers is a Euclidean string if the string (p0 + 1)p1...(pn-1 - 1) is rotationally equivalent (i.e., conjugate) to p. We show that Euclidean strings exist if and only if n and p0 + p1 + ... + pn-1 are relatively prime and that, if they exist, they are unique. We show how to construct them using an algorithm with the same structure as the Euclidean algorithm, hence the name. We show that Euclidean strings are Lyndon words and we describe relationships between Euclidean strings and the Stem-Brocot tree, Fibonacci strings, Beatty sequences, and Sturmian sequences. We also describe an application to a graph embedding problem.