Geodesic
A family of two-dimensional words with maximal pattern complexity~$2k$
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 3-14

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Maximal pattern complexity $p^*(k)$ is one of the counting functions over infinite words. In this paper we consider it over two-dimensional words. We construct an infinite family of two-dimensional words with the maximal pattern complexity $p^*(k)=2k$ for $k\in\mathbb N$. It is the minimum of maximal pattern complexity over two-dimensional and not two-periodic words. Bibliogr. 21.
Keywords: complexity, maximal pattern complexity, two-dimensional word, Toeplitz word. 
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     author = {Ts. Ch.-D. Batueva},
     title = {A family of two-dimensional words with maximal pattern complexity~$2k$},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {17},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2010_17_5_a0/}
}
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Ts. Ch.-D. Batueva. A family of two-dimensional words with maximal pattern complexity~$2k$. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 3-14. http://geodesic.mathdoc.fr/item/DA_2010_17_5_a0/