Recurrence in Multidimensional Words
| Autor: | Elise Vandomme, Svetlana Puzynina, Emilie Charlier |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
050101 languages & linguistics
Series (mathematics) Computer science 05 social sciences Block (permutation group theory) 02 engineering and technology Fixed point Square (algebra) Prefix Combinatorics Morphism Bounded function 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Computer Science::Formal Languages and Automata Theory Word (group theory) |
| Zdroj: | Language and Automata Theory and Applications ISBN: 9783030134341 LATA |
| DOI: | 10.1007/978-3-030-13435-8_29 |
| Popis: | 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 \((n_1,\ldots ,n_d)\in \mathbb {N}^d\) there exists \(N\in \mathbb {N}\) such that each block of size \((N,\ldots ,N)\) contains the prefix of size \((n_1,\ldots ,n_d)\). We introduce and study a new notion of uniform recurrence of multidimensional infinite words: for each rational slope \((q_1,\ldots ,q_d)\), each rectangular prefix must occur along this slope, that is in positions \(\ell (q_1,\ldots ,q_d)\), 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. |
| Databáze: | OpenAIRE |
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