Geodesic
Monomer-dimer tatami tilings of rectangular regions
The electronic journal of combinatorics, Tome 18 (2011) no. 1

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl EuDML
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.
DOI : 10.37236/596
Classification : 52C20, 05B45, 05A19
Mots-clés : tatami, monomer-dimer tiling, rational generating function 
Alejandro Erickson; Frank Ruskey; Jennifer Woodcock; Mark Schurch. Monomer-dimer tatami tilings of rectangular regions. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/596
@article{10_37236_596,
     author = {Alejandro Erickson and Frank Ruskey and Jennifer Woodcock and Mark Schurch},
     title = {Monomer-dimer tatami tilings of rectangular regions},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/596},
     zbl = {1215.52009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/596/}
}
TY  - JOUR
AU  - Alejandro Erickson
AU  - Frank Ruskey
AU  - Jennifer Woodcock
AU  - Mark Schurch
TI  - Monomer-dimer tatami tilings of rectangular regions
JO  - The electronic journal of combinatorics
PY  - 2011
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/596/
DO  - 10.37236/596
ID  - 10_37236_596
ER  - 
%0 Journal Article
%A Alejandro Erickson
%A Frank Ruskey
%A Jennifer Woodcock
%A Mark Schurch
%T Monomer-dimer tatami tilings of rectangular regions
%J The electronic journal of combinatorics
%D 2011
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/596/
%R 10.37236/596
%F 10_37236_596

Cité par Sources :