Geometric Containment and Partial Orders
Nicola Santoro, Jeffrey B. Sidney, S. J. Sidney, Jorge Urrutia · SIAM Journal on Discrete Mathematics · 1989
Given two geometric sets A and B, it is said that A is containable in B provided A is isometric to a subset of B. Containability induces a partial order on any set of geometric figures, such as rectangles in the plane. A recent result states that for the set of rectangles in the plane, the containability partial order is of countably infinite dimension. In this paper the rectangle result is extended to other families of geometric figures and to a partial order obtained from quadratic polynomials.