Arithmetical closure of two dimensional Toeplitz words
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 2, pp. 3-15.

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The arithmetical closure of a word is the set of all subwords of its arithmetical subsequences. In this paper we study the arithmetical closure of two-dimensional Toeplitz words. We find an explicit formula for the arithmetical complexity for some set of Toeplitz words. Bibl. 11.
Keywords: complexity, arithmetical complexity, two dimensional words, Toeplitz's words.
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Ts. C.-D. Batueva. Arithmetical closure of two dimensional Toeplitz words. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 2, pp. 3-15. http://geodesic.mathdoc.fr/item/DA_2009_16_2_a0/

[1] Allouche J.-P., Baake M., Cassaigne J., Damanik D., “Palindrom complexity”, Theoret. Comput. Sci., 292 (2003), 9–31 | DOI | MR | Zbl

[2] Avgustinovich S. V., Cassaigne J., Frid A. E., “Sequences of low arithmetical complexity”, Theoret. Informatics Appl., 40:4 (2006), 569–582 | DOI | MR | Zbl

[3] Avgustinovich S. V., Fon-Der-Flaass D. G., Frid A. E., “Arithmetical complexity of infinite words”, Words, Languages Combinatorics (ICWLC 2000), III (Kyoto, Japan, 2000, March 14–18), World Scientific Publishing, Singapore, 2003, 51–62 | MR

[4] Cassaigne J., “Double sequences with complexity $mn+1$”, J. Autom. Lang. Comb., 4:3 (1999), 153–170 | MR | Zbl

[5] Cassaigne J., Karhumäki J., “Toeplitz words, generalized periodicity and periodically iterated morphisms”, European J. Combin., 18 (1997), 497–510 | DOI | MR | Zbl

[6] Ferenczi S., “Complexity of sequences and dynamical systems”, Discrete Math., 206 (1999), 145–154 | DOI | MR | Zbl

[7] Frid A. E., “Arithmetical complexity of symmetric DOL words”, Theoret. Comput. Sci., 306 (2003), 535–542 | DOI | MR | Zbl

[8] Kamae T., Zamboni L., “Sequence entropy and the maximal pattern complexity of infinite words”, Ergodic Theory Dynam. System., 22 (2002), 1191–1199 | MR | Zbl

[9] Koskas M., “Complexités de suites de Toeplitz”, Discrete Math., 183 (1998), 161–183 | DOI | MR | Zbl

[10] Nakashima I., Tamura J.-I., Yasutomi S.-I., “$^\ast$-Sturmian words and complexity”, J. Theórie des Nombres de Bordeaux, 15 (2003), 767–804 | MR | Zbl

[11] Restivo A., Salemi S., “Binary patterns in infinite binary words”, Formal and Natural Computing, Lect. Notion in Comput. Sci., 2300, Springer, Berlin, 2002, 107–118 | MR