Lexicographically least words in the orbit closure of the Rudin-Shapiro word
James D. Currie
TL;DR
This paper characterizes the lexicographically least words in the orbit closure of the Rudin-Shapiro word, providing an explicit description and answering a previously open question.
Contribution
It offers an effective characterization of the lexicographically least words in the orbit closure of the Rudin-Shapiro word, including an explicit form 0w.
Findings
The lexicographically least word in the orbit closure is 0w.
Provides an explicit description of the least word with a given prefix.
Answers an open question by Allouche et al.
Abstract
We give an effective characterization of the lexicographically least word in the orbit closure of the Rudin-Shapiro word w having a specified prefix. In particular, the lexicographically least word in the orbit closure of the Rudin-Shapiro word is 0w. This answers a question Allouche et al.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Authorship Attribution and Profiling