Figure 1 - uploaded by Sidharth Dhawan
Content may be subject to copyright.
Source publication
![Figure 3: All pentominoes, with the U highlighted. Taken from [9]](profile/Sidharth-Dhawan/publication/51966025/figure/fig3/AS:305891007057933@1449941507894/All-pentominoes-with-the-U-highlighted-Taken-from-9_Q320.jpg)
Polyominoes are a subset of polygons which can be constructed from
integer-length squares fused at their edges. A system of polygons P is
interlocked if no subset of the polygons in P can be removed arbitrarily far
away from the rest. It is already known that polyominoes with four or fewer
squares cannot interlock. It is also known that determining...
Context in source publication
Context 1
... that a system of polygons is rigid is stronger than claiming they are not interlocked, because in a rigid system no polygon can be displaced at all, whereas interlocked polygons can be displaced a finite distance relative to each other (though not an infinite distance). We now turn our attention to special classes of polyominoes. These classes will be mentioned in the proofs, since some classes can be spread apart more easily. We define a class of polygons that can be easily separated in just one direction. A polygon is monotone in direction θ if the region of intersection of the polygon with any line drawn perpendicular to θ is no more than one connected line segment, as shown in Figure 1. Some polyominoes are also monotone in both the x and y directions, which makes them even easier to separate from other polyominoes. An orthogonal polygon is orthogonally convex if it is monotonic in both the x and y ...
Similar publications
A famous result of D. Walkup states that the only rectangles that may be
tiled by the T-tetromino are those in which both sides are a multiple of four.
In this paper we examine the rest of the rectangles, asking how many
T-tetrominos may be placed into those rectangles without overlap, or,
equivalently, what is the least number of gaps that need to...
