# Combinatorics of standard Sturmian words

• Aldo de Luca
Combinatorics of Words
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1261)

## 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.

## Key words

Sturmian words standard words standard morphisms

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