Langford strings are square-free

Research output: Contribution to journalArticle


Given a set Vn={v1,…,vn} of n symbols, a sequence x= x1x2…xm is called a weak Langford string if xi∊ Vnfor 1≤i≤m, and any two consecutive occurrences of vjin x are separated by precisely j characters of x, 1≤i≤m. Proving subsequent conjectures of Păun [5] and Marcus and Păun [4], we show that every weak Langford string is square-free. As a consequence, all Langford languages are finite. Some related questions are raised.

Original languageEnglish
Pages (from-to)75-78
Number of pages4
JournalInternational Journal of Computer Mathematics
Issue number2-4
Publication statusPublished - Jan 1989


  • Langford string
  • Square-free language
  • finite language

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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