Langford strings are square-free

Research output: Contribution to journalArticle

Abstract

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
Volume29
Issue number2-4
DOIs
Publication statusPublished - 1989

Fingerprint

Square free
Strings
Consecutive
Language
Character

Keywords

  • finite language
  • Langford string
  • Square-free language

ASJC Scopus subject areas

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

Cite this

Langford strings are square-free. / Tuza, Z.

In: International Journal of Computer Mathematics, Vol. 29, No. 2-4, 1989, p. 75-78.

Research output: Contribution to journalArticle

@article{f4fe67cb16df4d8eb993e77b77c53d45,
title = "Langford strings are square-free",
abstract = "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.",
keywords = "finite language, Langford string, Square-free language",
author = "Z. Tuza",
year = "1989",
doi = "10.1080/00207168908803750",
language = "English",
volume = "29",
pages = "75--78",
journal = "International Journal of Computer Mathematics",
issn = "0020-7160",
publisher = "Taylor and Francis Ltd.",
number = "2-4",

}

TY - JOUR

T1 - Langford strings are square-free

AU - Tuza, Z.

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

KW - finite language

KW - Langford string

KW - Square-free language

UR - http://www.scopus.com/inward/record.url?scp=84948267471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948267471&partnerID=8YFLogxK

U2 - 10.1080/00207168908803750

DO - 10.1080/00207168908803750

M3 - Article

VL - 29

SP - 75

EP - 78

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 2-4

ER -