Abstract
The conjugation class of a special Sturmian morphism carries a natural linear order by virtue of the two elementary conjugations \(conj_a\) and \(conj_b\) with the single letters a and b, with the standard morphism of the class as the smallest element in this order. We show that a lexicographic order on the morphisms of the given conjugation class can be defined that matches the conjugation order.
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Notes
- 1.
The setting \(\tilde{\mathcal {G}} < \mathcal {D}\) is arbitrary here. It could be likewise \(\mathcal {D} < \tilde{\mathcal {G}}\) without consequences for the content of the article.
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Clampitt, D., Noll, T. (2017). Matching Lexicographic and Conjugation Orders on the Conjugation Class of a Special Sturmian Morphism. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_9
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DOI: https://doi.org/10.1007/978-3-319-66396-8_9
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