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Associative shuffle of infinite words. (English) Zbl 0884.68071
Mycielski, Jan (ed.) et al., Structures in logic and computer science. A selection of essays in honor of Andrzej Ehrenfeucht (65th birthday on August 8, 1997). Berlin: Springer. Lect. Notes Comput. Sci. 1261, 291-307 (1997).
Summary: Some shuffle-like operations on infinite (\(\omega\)-words) are investigated. The operations are introduced using a uniform method based on the notion of an \(\omega\)-trajectory. We prove an interconnection between associative closure of shuffle on \(\omega\)-trajectories and periodicity of \(\omega\)-words. This provides a characterization of the ultimately periodic \(\omega\)-words. Finally, a remarkable property of the Fibonacci \(\omega\)-word is exhibited.
For the entire collection see [Zbl 0868.00014].

68Q45 Formal languages and automata
68R15 Combinatorics on words