# MUIC Math

Mathematics at MUIC

### Internal

seminar:ma_tiling

# Tiling with fences

Michael A. Allen
Physics Department, Mahidol University, Bangkok

### Abstract

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.