Petr Ambrož ; Anna Frid ; Zuzana Masáková ; Edita Pelantová - On the number of factors in codings of three interval exchange

dmtcs:553 - Discrete Mathematics & Theoretical Computer Science, November 9, 2011, Vol. 13 no. 3 - https://doi.org/10.46298/dmtcs.553
On the number of factors in codings of three interval exchangeArticle

Authors: Petr Ambrož 1; Anna Frid 2; Zuzana Masáková 1; Edita Pelantová ORCID1

  • 1 Doppler Institute/ Department of Mathematics
  • 2 Sobolev Institute of Mathematics

We consider exchange of three intervals with permutation (3, 2, 1). The aim of this paper is to count the cardinality of the set 3iet (N) of all words of length N which appear as factors in infinite words coding such transformations. We use the strong relation of 3iet words and words coding exchange of two intervals, i.e., Sturmian words. The known asymptotic formula #2iet(N)/N-3 similar to 1/pi(2) for the number of Sturmian factors allows us to find bounds 1/3 pi(2) +o(1) \textless= #3iet(N)N-4 \textless= 2 pi(2) + o(1)


Volume: Vol. 13 no. 3
Section: Graph Theory
Published on: November 9, 2011
Accepted on: June 9, 2015
Submitted on: April 24, 2009
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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