Mathematics – Combinatorics
Scientific paper
2008-05-27
Mathematics
Combinatorics
16 pages, submit to TCS
Scientific paper
Sturmian sequences are well-known as the ones having minimal complexity over a 2-letter alphabet. They are also the balanced sequences over a 2-letter alphabet and the sequences describing discrete lines. They are famous and have been extensively studied since the 18th century. One of the {extensions} of these sequences over a $k$-letter alphabet, with $k\geq 3$, are the episturmian sequences, which generalizes a construction of Sturmian sequences using the palindromic closure operation. There exists a finite version of the Sturmian sequences called the Christoffel words. They are known since the works of Christoffel and have interested many mathematicians. In this paper, we introduce a generalization of Christoffel words for an alphabet with 3 letters or more, using the episturmian morphisms. We call them the {\it epichristoffel words}. We define this new class of finite words and show how some of the properties of the Christoffel words can be generalized naturally or not for this class.
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