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- W2912135878 abstract "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 (Nin 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." @default.
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- W2912135878 date "2019-01-01" @default.
- W2912135878 modified "2023-09-23" @default.
- W2912135878 title "Recurrence in Multidimensional Words" @default.
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- W2912135878 doi "https://doi.org/10.1007/978-3-030-13435-8_29" @default.
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