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A Proof of Shur’s Conjecture on the Growth of Power-Free Languages over Large Alphabets

Authors Vuong Bui, Matthieu Rosenfeld

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics on words
Keywords
  • power-free languages
  • large alphabets
  • Shur’s conjecture
  • Dejean’s conjecture

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Abstract

We settle a conjecture of Shur on an estimation of the exponential growth rates of the languages of (n/(n-1))-free words and (n/(n-1)) ^+-free words over large alphabets of size k with a correction of order O (1/(k²)).

Cite As Get BibTex

Vuong Bui and Matthieu Rosenfeld. A Proof of Shur’s Conjecture on the Growth of Power-Free Languages over Large Alphabets. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 32:1-32:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.32

Author Details

Vuong Bui
  • UET, Vietnam National University, Hanoi, 144 Xuan Thuy Street, Hanoi, 100000, Vietnam
Matthieu Rosenfeld
  • LIRMM, Université de Montpellier, CNRS, 161 Rue Ada, 34095, Montpellier, France

References

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