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  • 标题:Disjunctive Omega-Words and Real Numbers
  • 本地全文:下载
  • 作者:Peter Hertling
  • 期刊名称:Journal of Universal Computer Science
  • 印刷版ISSN:0948-6968
  • 出版年度:1996
  • 卷号:2
  • 期号:7
  • 页码:549-568
  • 出版社:Graz University of Technology and Know-Center
  • 摘要:An ω-word p over a finite alphabet Σ is called disjunctive if every finite word over Σ occurs as a subword in p. A real number is called disjunctive to base a if it has a disjunctive a-adic expansion. For every pair of integers a,b ≥ 2 such that there exist numbers disjunctive to base a but not to base b we explicitly construct very simple examples of such numbers. General versions of the following results are proved. If (ni)i∈ω is a strictly increasing sequence of positive integers with ni+1 ≥ 3ni for infinitely many i then Σ 3-ni is disjunctive to base 2. The number Σ2-i!-i is disjunctive to base a if a is even and not a power of 2. The sum Σ2-ci is disjunctive to base 6 if c ≥ 3 is odd.
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