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標題: Properties of Fibonacci languages
作者: Yu, S.S.
Zhao, Y.K.
關鍵字: Fibonacci word;primitive;palindrome word;code;context-free
Project: Discrete Mathematics
期刊/報告no:: Discrete Mathematics, Volume 224, Issue 1-3, Page(s) 215-223.
The Fibonacci language F-u,F-nu is the set of all Fibonacci words, where the first word and the second word in the Fibonacci sequence are u and nu, respectively. We show that the language F-u,F-nu is context-free free. We also show that F-u,F-nu is not dense if the word u nu contains at least two distinct letters. Let w(i) denote the ith Fibonacci word. When considering the Fibonacci language F-a,F-b for two distinct letters a and b, we show that for k greater than or equal to 2 and 1 less than or equal to i < k, the word w(i)w(i) is not a prefix of the Fibonacci word w(k). We also show that for k greater than or equal to 2, the language F-k = {w(nk) / n greater than or equal to 1} is a code. (C) 2000 Elsevier Science B.V. All rights reserved.
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00089-3
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