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On Infinite Prefix Normal Words.

Ferdinando Cicalese1, Zsuzsanna Lipták1, Massimiliano Rossi2

  • 1Department of Computer Science, University of Verona, Verona, Italy.

Theoretical Computer Science
|June 24, 2021
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Summary
This summary is machine-generated.

This study explores infinite prefix normal words, a type of binary word. We reveal connections between prefix normality, Sturmian words, abelian complexity, and lexicographic order.

Keywords:
Sturmian wordsThue-Morse sequenceabelian complexitycombinatorics on wordsinfinite wordslexicographic orderpaperfolding wordprefix normal words

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Area of Science:

  • Theoretical Computer Science
  • Combinatorics on Words

Background:

  • Prefix normal words are binary words where no factor has more 1s than a prefix of the same length.
  • Finite prefix normal words were previously defined, but infinite cases remained less explored.

Purpose of the Study:

  • To investigate the properties of infinite prefix normal words.
  • To establish relationships between prefix normal words and other significant classes of infinite binary words.

Main Methods:

  • Analysis of binary word properties.
  • Comparison with known word classes like Sturmian words.
  • Investigation of abelian complexity and lexicographic ordering.

Main Results:

  • Established a connection between prefix normal words and Sturmian words.
  • Demonstrated a link between prefix normality and abelian complexity.
  • Explored the relationship between prefix normality and lexicographic order.

Conclusions:

  • Infinite prefix normal words exhibit significant connections to established concepts in combinatorics on words.
  • The study expands the understanding of binary word structures and their properties.