Involutions of epicentral words

Episturmian sequences, or words, are a natural generalization of Sturmian sequences to arbitrary finite alphabets. In this paper we investigate various combinatorial properties of epicentral words, i.e., palindromic prefixes of standard episturmian words. We consider the action of certain involutions defined on epicentral words. We show that in some cases their fixed points may be characterized in terms of suitable faithful representations of epicentral words. We further show that various previously known results for central Sturmian words may be extended to epicentral words.

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