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 -
On the number of factors in codings of three interval exchange

Authors: Petr Ambrož 1; Anna Frid 2; Zuzana Masáková 1; Edita Pelantová ORCID-iD1

  • 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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Source : ScholeXplorer IsRelatedTo DOI 10.1007/bf02893083
  • 10.1007/bf02893083
Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories

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