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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
Summary
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.
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.
Keywords:
Sturmian wordsThue-Morse sequenceabelian complexitycombinatorics on wordsinfinite wordslexicographic orderpaperfolding wordprefix normal wordsMore Related Videos
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