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- W2954641277 abstract "In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A $d$-dimensional word is called emph{uniformly recurrent} if for all $(s_1,ldots,s_d)inmathbb{N}^d$ there exists $ninmathbb{N}$ such that each block of size $(n,ldots,n)$ contains the prefix of size $(s_1,ldots,s_d)$. We are interested in a modification of this property. Namely, we ask that for each rational direction $(q_1,ldots,q_d)$, each rectangular prefix occurs along this direction in positions $ell(q_1,ldots,q_d)$ with bounded gaps. Such words are called emph{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 multidimentional rotation words and of fixed points of square morphisms." @default.
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- W2954641277 date "2019-06-29" @default.
- W2954641277 modified "2023-09-27" @default.
- W2954641277 title "Recurrence along directions in multidimensional words" @default.
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