Elsevier

Discrete Applied Mathematics

Volume 214, 11 December 2016, Pages 63-87
Discrete Applied Mathematics

Markov word patterns and a relation on α-words

https://doi.org/10.1016/j.dam.2016.05.032Get rights and content
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Abstract

We prove that all suffixes of a two-way infinite extension of an irrational characteristic word can be represented as Markov word patterns (MWPs) of type 1 and under some conditions, as MWPs of type 2. For each of these MWPs, the pairs of seed words are identified and are described in several different ways. We prove that the simple Sturmian words are the only Sturmian words that are representable as MWPs, each pair of seed words of which is either a pair of adjacent α-words or adjacent α-words with reverse order.

Keywords

Irrational characteristic word
Adjacent α-word
Markov word pattern
Seed word
Simple Sturmian word

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