A note on the Markoff condition and central words
Amy Glen, Aaron Lauve, Franco V. Saliola
TL;DR
This paper introduces Markoff words as factors in bi-infinite words satisfying the Markoff condition and proves they are equivalent to central words, providing a new way to characterize Christoffel words.
Contribution
It establishes the equivalence between Markoff words and central words, offering a novel characterization of Christoffel words.
Findings
Markoff words coincide with central words
New characterization of Christoffel words
Provides insights into the structure of bi-infinite words
Abstract
We define Markoff words as certain factors appearing in bi-infinite words satisfying the Markoff condition. We prove that these words coincide with central words, yielding a new characterization of Christoffel words.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Geometric and Algebraic Topology