In this note we consider an Erdos-Ko-Rado analog of tilings. Namely, given two tilings of a common region we say that they intersect if they have at least one tile in the same location. We show that for a domino tiling of the 2 x n strip that the largest collection of tilings which pairwise intersect are counted by the Fibonacci numbers. We also solve the problem for tilings of the 3x(2n) strip using dominoes.
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St.Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. PetersburgSt.Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg
Aksenov V.
Kokhas K.
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St.Petersburg State University, St. PetersburgSt.Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg
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College of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo,153-8914, JapanCollege of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo,153-8914, Japan
Kamio, Yuhi
Koizumi, Junnosuke
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Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo,153-8914, JapanCollege of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo,153-8914, Japan
Koizumi, Junnosuke
Nakazawa, Toshihiko
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KADOKAWA DWANGO Educational Institute, Kabuki-za Tower 14F, 4-12-15 Ginza, Chuo-ku, Tokyo,104-0061, JapanCollege of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo,153-8914, Japan