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On Column-Convex and Convex Carlitz Polyominoes


In this paper, we introduce and study Carlitz polyominoes. In particular, we show that, as n grows to infinity, asymptotically the number of

  1. (1)

    column-convex Carlitz polyominoes with perimeter 2n is

    $$\begin{aligned} \frac{9\sqrt{2}(14+3\sqrt{3})}{2704\sqrt{\pi n^3}}4^n. \end{aligned}$$
  2. (2)

    convex Carlitz polyominoes with perimeter 2n is

    $$\begin{aligned} \frac{n+1}{10}\left( \frac{3+\sqrt{5}}{2}\right) ^{n-2}. \end{aligned}$$

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Mansour, T., Rastegar, R. & Shabani, A.S. On Column-Convex and Convex Carlitz Polyominoes. Math.Comput.Sci. 15, 889–898 (2021).

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  • Carlitz polyominoes

Mathematics Subject Classification

  • 05B50
  • 05A16