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On Column-Convex and Convex Carlitz Polyominoes

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 3498838, Haifa, Israel

    Toufik Mansour

  2. Occidental Petroleum Corporation, Houston, TX, 77046, USA

    Reza Rastegar

  3. Departments of Mathematics and Engineering, University of Tulsa, Tulsa, OK, 74104, USA

    Reza Rastegar

  4. Department of Mathematics, University of Prishtina, 10000, Prishtinë, Republic of Kosovo

    Armend Sh. Shabani

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  1. Toufik Mansour
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  2. Reza Rastegar
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  3. Armend Sh. Shabani
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Correspondence to Toufik Mansour.

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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). https://doi.org/10.1007/s11786-021-00518-z

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