Minimal unique expansions with digits in ternary alphabets

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• 作者：Anna Chiara Lai^a ; ^{annachiara.lai@uniroma1.it"" rel=""nofollow} ; ^{lai@dmmm.uniroma1.it"" rel=""nofollow}
• 关键词：Ternary alphabet ; Unique expansion ; Noninteger base ; Beta-expansion ; Critical base ; Greedy expansion ; Lazy expansion ; Univoque sequence ; Balanced sequences
• 刊名：Indagationes Mathematicae
• 出版年：2011
• 出版时间：July 2011
• 年：2011
• 卷：21
• 期：1-2
• 页码：1-15
• 全文大小：221 K

文摘

The study of the redundancy of non-integer base numeration systems involves several fields of mathematics and of theoretical computer science, including number theory, ergodic theory, topology, and combinatorics on words. When the base is smaller than a sharp value, called critical base, only trivial expansions in a non-integer base are unique, while for greater bases there exist some non-trivial unique expansions. By investigating an unexpected relation between balanced sequences and unique expansions, we explicitly characterize for a large class of three-letter alphabets the minimal unique expansions, namely those unique expansions that first appear when we choose bases larger than the critical base.