Squares and cubes in Sturmian sequences

Artūras Dubickas

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 3, page 615-624
  • ISSN: 0988-3754

Abstract

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We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.

How to cite

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Dubickas, Artūras. "Squares and cubes in Sturmian sequences." RAIRO - Theoretical Informatics and Applications 43.3 (2009): 615-624. <http://eudml.org/doc/250615>.

@article{Dubickas2009,
abstract = { We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares. },
author = {Dubickas, Artūras},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Sturmian word; block-complexity; stammering word.; stammering word},
language = {eng},
month = {3},
number = {3},
pages = {615-624},
publisher = {EDP Sciences},
title = {Squares and cubes in Sturmian sequences},
url = {http://eudml.org/doc/250615},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Dubickas, Artūras
TI - Squares and cubes in Sturmian sequences
JO - RAIRO - Theoretical Informatics and Applications
DA - 2009/3//
PB - EDP Sciences
VL - 43
IS - 3
SP - 615
EP - 624
AB - We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.
LA - eng
KW - Sturmian word; block-complexity; stammering word.; stammering word
UR - http://eudml.org/doc/250615
ER -

References

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