Author:
Erickson Alejandro,Ruskey Frank,Woodcock Jennifer,Schurch Mark
Abstract
In this paper we consider tilings of rectangular regions with two types of tiles, $1 \times 2$ tiles (dimers) and $1 \times 1$ tiles (monomers). The tiles must cover the region and satisfy the constraint that no four corners of the tiles meet; such tilings are called tatami tilings. We provide a structural characterization and use it to prove that the tiling is completely determined by the tiles that are on its border. We prove that the number of tatami tilings of an $n \times n$ square with $n$ monomers is $n2^{n-1}$. We also show that, for fixed-height, the generating function for the number of tatami tilings of a rectangle is a rational function, and outline an algorithm that produces the generating function.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献