On Tilings of Quadrants and Rectangles and Rectangular Pattern

Viorel Nitica
2016 Open Journal of Discrete Mathematics  
The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from
more » ... ce appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these ( ) 1 gcd , n k n < < . Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.
doi:10.4236/ojdm.2016.64028 fatcat:4fwvvqkzvzccla7cyvbebrnleq