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Abelian closures of infinite binary words. / Puzynina, Svetlana; Whiteland, Markus A.

In: Journal of Combinatorial Theory. Series A, Vol. 185, 105524, 01.2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Puzynina, S & Whiteland, MA 2022, 'Abelian closures of infinite binary words', Journal of Combinatorial Theory. Series A, vol. 185, 105524. https://doi.org/10.1016/j.jcta.2021.105524

APA

Puzynina, S., & Whiteland, M. A. (2022). Abelian closures of infinite binary words. Journal of Combinatorial Theory. Series A, 185, [105524]. https://doi.org/10.1016/j.jcta.2021.105524

Vancouver

Puzynina S, Whiteland MA. Abelian closures of infinite binary words. Journal of Combinatorial Theory. Series A. 2022 Jan;185. 105524. https://doi.org/10.1016/j.jcta.2021.105524

Author

Puzynina, Svetlana ; Whiteland, Markus A. / Abelian closures of infinite binary words. In: Journal of Combinatorial Theory. Series A. 2022 ; Vol. 185.

BibTeX

@article{c0e6fc36531b4dcebfef30a8c9bb8e93,
title = "Abelian closures of infinite binary words",
abstract = "Two finite words u and v are called Abelian equivalent if each letter occurs equally many times in both u and v. The abelian closure A(x) of (the shift orbit closure of) an infinite word x is the set of infinite words y such that, for each factor u of y, there exists a factor v of x which is abelian equivalent to u. The notion of an abelian closure gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which A(x) equals the shift orbit closure Ω(x). In this paper we show that, contrary to larger alphabets, the abelian closure of a uniformly recurrent aperiodic binary word which is not Sturmian contains infinitely many minimal subshifts.",
keywords = "Abelian equivalence, Infinite words, Sturmian words, Subshifts, COMPLEXITY",
author = "Svetlana Puzynina and Whiteland, {Markus A.}",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2022",
month = jan,
doi = "10.1016/j.jcta.2021.105524",
language = "English",
volume = "185",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Abelian closures of infinite binary words

AU - Puzynina, Svetlana

AU - Whiteland, Markus A.

N1 - Publisher Copyright: © 2021 Elsevier Inc.

PY - 2022/1

Y1 - 2022/1

N2 - Two finite words u and v are called Abelian equivalent if each letter occurs equally many times in both u and v. The abelian closure A(x) of (the shift orbit closure of) an infinite word x is the set of infinite words y such that, for each factor u of y, there exists a factor v of x which is abelian equivalent to u. The notion of an abelian closure gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which A(x) equals the shift orbit closure Ω(x). In this paper we show that, contrary to larger alphabets, the abelian closure of a uniformly recurrent aperiodic binary word which is not Sturmian contains infinitely many minimal subshifts.

AB - Two finite words u and v are called Abelian equivalent if each letter occurs equally many times in both u and v. The abelian closure A(x) of (the shift orbit closure of) an infinite word x is the set of infinite words y such that, for each factor u of y, there exists a factor v of x which is abelian equivalent to u. The notion of an abelian closure gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which A(x) equals the shift orbit closure Ω(x). In this paper we show that, contrary to larger alphabets, the abelian closure of a uniformly recurrent aperiodic binary word which is not Sturmian contains infinitely many minimal subshifts.

KW - Abelian equivalence

KW - Infinite words

KW - Sturmian words

KW - Subshifts

KW - COMPLEXITY

UR - http://www.scopus.com/inward/record.url?scp=85113446454&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/73f4f5ad-b435-346e-b852-b7953422f534/

U2 - 10.1016/j.jcta.2021.105524

DO - 10.1016/j.jcta.2021.105524

M3 - Article

AN - SCOPUS:85113446454

VL - 185

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

M1 - 105524

ER -

ID: 86499228