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Diskretn. Anal. Issled. Oper., 2010, Volume 17, Number 5, Pages 3–14 (Mi da620)  

A family of two-dimensional words with maximal pattern complexity $2k$

Ts. Ch.-D. Batueva

Novosibirsk State University, Novosibirsk, Russia

Abstract: 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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Bibliographic databases:
UDC: 519.725
Received: 09.02.2009
Revised: 23.06.2010

Citation: Ts. Ch.-D. Batueva, “A family of two-dimensional words with maximal pattern complexity $2k$”, Diskretn. Anal. Issled. Oper., 17:5 (2010), 3–14

Citation in format AMSBIB
\Bibitem{Bat10}
\by Ts.~Ch.-D.~Batueva
\paper A family of two-dimensional words with maximal pattern complexity~$2k$
\jour Diskretn. Anal. Issled. Oper.
\yr 2010
\vol 17
\issue 5
\pages 3--14
\mathnet{http://mi.mathnet.ru/da620}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2779347}
\zmath{https://zbmath.org/?q=an:1249.68148}


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