Tilings by $1 \times{}            1$ and $2 \times{}          2$

Rolin, Nicolas; Ugolnikova, Alexandra

doi:10.1051/ita/2016011

Tilings by

1 \times 1

and

2 \times 2

Rolin, Nicolas ¹ ; Ugolnikova, Alexandra ¹

¹ LIPN, Paris 13, France

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 105-116

Résumé

We consider tilings of a $k \times n$ board by $1 \times 1$ and $2 \times 2$ squares and get combinatorical results on proportions of small squares for $k \leq 10$ in plain case and for $k \leq 8$ in cylindrical case.

Reçu le : 2016-03-24
Accepté le : 2016-04-06

MR Zbl

DOI : 10.1051/ita/2016011

Classification : 35L05, 35L70
Keywords: Tiling, square tiles, generating functions, automaton, strip tilings, tiling graph

Affiliations des auteurs :

Rolin, Nicolas ¹ ; Ugolnikova, Alexandra ¹

¹ LIPN, Paris 13, France

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     author = {Rolin, Nicolas and Ugolnikova, Alexandra},
     title = {Tilings by $1 \times{}            1$ and $2 \times{}          2$},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {105--116},
     year = {2016},
     publisher = {EDP Sciences},
     volume = {50},
     number = {1},
     doi = {10.1051/ita/2016011},
     zbl = {1346.05028},
     mrnumber = {3518163},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita/2016011/}
}

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Rolin, Nicolas; Ugolnikova, Alexandra. Tilings by $1 \times{}            1$ and $2 \times{}          2$. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 105-116. doi: 10.1051/ita/2016011

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