Regular episturmian words are analyzed for their initial nonrepetitive complexity and Diophantine exponents. The study reveals novel results on irrationality exponents, transcendental numbers, and Liouville numbers. The concept of Ostrowski numeration systems is introduced to represent these words efficiently.
The intercept of episturmian words is defined based on sequences of finite words, leading to a deeper understanding of their structure. Theorems are presented to characterize the properties of regular episturmian words and their numerical representations.
Key results include the relationship between partial quotients, greedy expansions, and Ostrowski expansions in the context of regular directive words. Theorems demonstrate how these concepts simplify the analysis of complex word structures.
Overall, the study sheds light on the intricate nature of regular episturmian words and provides a framework for efficient representation and analysis using generalized standard words.
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