Reference : Recurrence in multidimensional words
Scientific congresses and symposiums : Paper published in a journal
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/231727
Recurrence in multidimensional words
English
Charlier, Emilie mailto [Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes >]
Puzynina, Svetlana [Saint-Petersburg State University > > > >]
Vandomme, Elise mailto [Université de Liège - ULiège > Département de mathématique > Probabilités et statistique mathématique >]
2019
Lecture Notes in Computer Science
Springer
11417
397-408
Yes
International
0302-9743
1611-3349
Germany
13th International Conference on Language and Automata Theory and Applications (LATA)
25 - 29 March 2019
Saint-Peterburg
Russia
[en] Uniform recurrence ; multidimensional word ; multidimensional morphism
[en] In this paper we study various modifications of the notion of uniform recurrence in multidimensional infinite words. A d-dimensional infinite word is said to be uniformly recurrent if for each prefix, there exists a fixed size such that each block of this size contains the prefix.
We introduce and study a new notion of uniform recurrence of multidimensional infinite words: for each rational slope, each rectangular prefix must occur along this slope with bounded gaps. Such words are called uniformly recurrent along all directions. We provide several constructions of multidimensional infinite words satisfying this condition, and more generally, a series of three conditions on recurrence. We study general properties of these new notions and in particular we study the strong uniform recurrence of fixed points of square morphisms.
Researchers
http://hdl.handle.net/2268/231727
10.1007/978-3-030-13435-8_29

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