Mathematics at MUIC

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Tiling with fences

Michael A. Allen
Physics Department, Mahidol University, Bangkok


We look at tiling an $n$-board (a linear array of $n$ square cells of unit width) using square tiles and $(\frac12,g)$-fence tiles where $g\in\mathbb{Z}^+$. A $(\frac12,g)$-fence is composed of two pieces of width $\frac12$ separated by a gap of width $g$. Although originally introduced to give a new combinatorial interpretation of the Tribonacci numbers, tiling with fences and squares can also be used to describe strongly restricted permutations in a natural and intuitive way.


  • A Pascal-like triangle related to the Tribonacci numbers
  • Strongly restricted permutations and tiling with fences
  • Proofs That Really Count: The Art of Combinatorial Proof
Last modified: 2016/12/21 16:08

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