Markov word patterns and a relation on -words

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• 作者：Wai-Fong Chuan^a ; ^{waifong@cycu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Fang-Yi Liao^a ; ^{fyliao920@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Fei Yu^b ; ^{aypyufei@mail.ypu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Irrational characteristic word ; Adjacent αα-word ; Markov word pattern ; Seed word ; Simple Sturmian word
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：11 December 2016
• 年：2016
• 卷：214
• 期：Complete
• 页码：63-87
• 全文大小：980 K

文摘

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$\alpha$-words or adjacent α$\alpha$-words with reverse order.