On the number of factors in codings of three interval exchange

Graph Theory 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 co...

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Bibliographic Details
Published inDiscrete Mathematics and Theoretical Computer Science Vol. 13; no. 3; pp. 51 - 66
Main Authors Ambroz, Petr, Frid, Anna, Masakova, Zuzana, Pelantova, Edita
Format Journal Article
LanguageEnglish
Published Nancy DMTCS 01.11.2011
Discrete Mathematics & Theoretical Computer Science
Subjects
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Computer Science
Discrete Mathematics
Dynamical systems
Factorials
Mathematics
Permutations
Czech Republic
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Summary:Graph Theory 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)
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.553