Standard

Recurrence along directions in multidimensional words. / Charlier, Émilie; Puzynina, Svetlana; Vandomme, Élise.

In: Discrete Mathematics, Vol. 343, No. 10, 112006, 10.2020.

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

Harvard

Charlier, É, Puzynina, S & Vandomme, É 2020, 'Recurrence along directions in multidimensional words', Discrete Mathematics, vol. 343, no. 10, 112006. https://doi.org/10.1016/j.disc.2020.112006

APA

Charlier, É., Puzynina, S., & Vandomme, É. (2020). Recurrence along directions in multidimensional words. Discrete Mathematics, 343(10), [112006]. https://doi.org/10.1016/j.disc.2020.112006

Vancouver

Charlier É, Puzynina S, Vandomme É. Recurrence along directions in multidimensional words. Discrete Mathematics. 2020 Oct;343(10). 112006. https://doi.org/10.1016/j.disc.2020.112006

Author

Charlier, Émilie ; Puzynina, Svetlana ; Vandomme, Élise. / Recurrence along directions in multidimensional words. In: Discrete Mathematics. 2020 ; Vol. 343, No. 10.

BibTeX

@article{98de66360d884e149a4df4ffc82fe1cc,
title = "Recurrence along directions in multidimensional words",
abstract = "In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A d-dimensional word is called uniformly recurrent if for all (s1,…,sd)∈Nd there exists n∈N such that each block of size (n,…,n) contains the prefix of size (s1,…,sd). We are interested in a modification of this property. Namely, we ask that for each rational direction (q1,…,qd), each rectangular prefix occurs along this direction in positions ℓ(q1,…,qd) with bounded gaps. Such words are called uniformly recurrent along all directions. We provide several constructions of multidimensional words satisfying this condition, and more generally, a series of four increasingly stronger conditions. In particular, we study the uniform recurrence along directions of multidimensional rotation words and of fixed points of square morphisms.",
keywords = "Multidimensional morphisms, Multidimensional words, Uniform recurrence, SEQUENCES, TILINGS, COMBINATORICS",
author = "{\'E}milie Charlier and Svetlana Puzynina and {\'E}lise Vandomme",
year = "2020",
month = oct,
doi = "10.1016/j.disc.2020.112006",
language = "English",
volume = "343",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "10",

}

RIS

TY - JOUR

T1 - Recurrence along directions in multidimensional words

AU - Charlier, Émilie

AU - Puzynina, Svetlana

AU - Vandomme, Élise

PY - 2020/10

Y1 - 2020/10

N2 - In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A d-dimensional word is called uniformly recurrent if for all (s1,…,sd)∈Nd there exists n∈N such that each block of size (n,…,n) contains the prefix of size (s1,…,sd). We are interested in a modification of this property. Namely, we ask that for each rational direction (q1,…,qd), each rectangular prefix occurs along this direction in positions ℓ(q1,…,qd) with bounded gaps. Such words are called uniformly recurrent along all directions. We provide several constructions of multidimensional words satisfying this condition, and more generally, a series of four increasingly stronger conditions. In particular, we study the uniform recurrence along directions of multidimensional rotation words and of fixed points of square morphisms.

AB - In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A d-dimensional word is called uniformly recurrent if for all (s1,…,sd)∈Nd there exists n∈N such that each block of size (n,…,n) contains the prefix of size (s1,…,sd). We are interested in a modification of this property. Namely, we ask that for each rational direction (q1,…,qd), each rectangular prefix occurs along this direction in positions ℓ(q1,…,qd) with bounded gaps. Such words are called uniformly recurrent along all directions. We provide several constructions of multidimensional words satisfying this condition, and more generally, a series of four increasingly stronger conditions. In particular, we study the uniform recurrence along directions of multidimensional rotation words and of fixed points of square morphisms.

KW - Multidimensional morphisms

KW - Multidimensional words

KW - Uniform recurrence

KW - SEQUENCES

KW - TILINGS

KW - COMBINATORICS

UR - http://www.scopus.com/inward/record.url?scp=85086726135&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/38ab19c6-bea5-352c-8bb4-4fa73473acb6/

U2 - 10.1016/j.disc.2020.112006

DO - 10.1016/j.disc.2020.112006

M3 - Article

AN - SCOPUS:85086726135

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 10

M1 - 112006

ER -

ID: 62340716