Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
TILING RECTANGLES, CYLINDERS, AND MOBIUS PETER G. ANDERSON
 

Summary: TILING RECTANGLES, CYLINDERS, AND MOBIUS
STRIPS
PETER G. ANDERSON
Abstract. We present a method for determining the number of ways
various two-dimensional grids can be tiled using several small tile reper-
toires.
1. Problem Background and Definitions
Figure 1. Tile sets for problems 1, 2, 3, and 4.
How many ways may we tile an mn rectangular grid (i.e., graph paper)
using a pair of tile shapes from the repertoires show in Figure 1:
(1) Vertical dominoes and squares.
(2) L-trimonoes and squares.
(3) Large and small squares.
(4) Vertical and horizontal dominoes.
In all cases here, the short dimensions are 1 and the long dimensions are
2. We can modify the problem by identifying the top and bottom edges to
form a cylinder. We can identify the top and bottom edges with orientation
reversal to form a Mobius strip. (Exception: our problem-2, L-trimonoes,
cannot participate in the tilings of non-orientable surfaces.)
2. Our Approach

  

Source: Anderson, Peter G. - Department of Computer Science, Rochester Institute of Technology

 

Collections: Computer Technologies and Information Sciences