# A note on constructing infinite binary words with polynomial subword complexity

Francine Blanchet-Sadri; Bob Chen; Sinziana Munteanu

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2013)

- Volume: 47, Issue: 2, page 195-199
- ISSN: 0988-3754

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topBlanchet-Sadri, Francine, Chen, Bob, and Munteanu, Sinziana. "A note on constructing infinite binary words with polynomial subword complexity." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 47.2 (2013): 195-199. <http://eudml.org/doc/273080>.

@article{Blanchet2013,

abstract = {Most of the constructions of infinite words having polynomial subword complexity are quite complicated, e.g., sequences of Toeplitz, sequences defined by billiards in the cube, etc. In this paper, we describe a simple method for constructing infinite words w over a binary alphabet \{ a,b \} with polynomial subword complexity pw. Assuming w contains an infinite number of a’s, our method is based on the gap function which gives the distances between consecutive b’s. It is known that if the gap function is injective, we can obtain at most quadratic subword complexity, and if the gap function is blockwise injective, we can obtain at most cubic subword complexity. Here, we construct infinite binary words w such that pw(n) = Θ(nβ) for any real number β > 1.},

author = {Blanchet-Sadri, Francine, Chen, Bob, Munteanu, Sinziana},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {binary words; subword complexity; gap function},

language = {eng},

number = {2},

pages = {195-199},

publisher = {EDP-Sciences},

title = {A note on constructing infinite binary words with polynomial subword complexity},

url = {http://eudml.org/doc/273080},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Blanchet-Sadri, Francine

AU - Chen, Bob

AU - Munteanu, Sinziana

TI - A note on constructing infinite binary words with polynomial subword complexity

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 2

SP - 195

EP - 199

AB - Most of the constructions of infinite words having polynomial subword complexity are quite complicated, e.g., sequences of Toeplitz, sequences defined by billiards in the cube, etc. In this paper, we describe a simple method for constructing infinite words w over a binary alphabet { a,b } with polynomial subword complexity pw. Assuming w contains an infinite number of a’s, our method is based on the gap function which gives the distances between consecutive b’s. It is known that if the gap function is injective, we can obtain at most quadratic subword complexity, and if the gap function is blockwise injective, we can obtain at most cubic subword complexity. Here, we construct infinite binary words w such that pw(n) = Θ(nβ) for any real number β > 1.

LA - eng

KW - binary words; subword complexity; gap function

UR - http://eudml.org/doc/273080

ER -

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