Abstract
In the present paper we develop a formalism to generate multi-dimensional words using lattices which generalizes the construction of real numbers (one-dimensional words) from a sequence of partial quotients using continued fractions. The construction was introduced in a special case by Simpson and Tijdeman in order to derive a multi-dimensional generalization of the theorem of Fine and Wilf. We show that the produced multi-dimensional words are intrinsically connected with k-dimensional Sturmian words.
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