Abstract
We overview some recent developments of the theory of Sturmian words showing that the ’kernel’ of the theory is the combinatorics of the set PER of all finite words ω on the alphabet A={a,b} having two periods p and q which are coprimes and such that |w|=p+q-2. The elements of PER have many surprising structural properties. In particular, the relation Stand=A U PER ab, ba holds, where Stand is the set of all finite standard Sturmian words. Moreover, PER can be generated by two different procedures. The first uses the operator of left palindrome closure, whereas the second uses some elementary standard morphisms. We prove the existence of a basic correspondence, that we call standard, between these two methods.
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de Luca, A. (1997). Combinatorics of standard Sturmian words. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds) Structures in Logic and Computer Science. Lecture Notes in Computer Science, vol 1261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63246-8_15
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DOI: https://doi.org/10.1007/3-540-63246-8_15
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