Adding Layers to Bumped-Body Polyforms with Minimum Perimeter Preserves Minimum Perimeter

In two dimensions, a polyform is a finite set of edge-connected cells on a square, triangular, or hexagonal grid. A layer is the set of grid cells that are vertex-adjacent to the polyform and not part of the polyform. A bumped-body polyform has two parts: a body and a bump. Adding a layer to a bumped-body polyform with minimum perimeter constructs a bumped-body polyform with min perimeter; the triangle case requires additional assumptions. A similar result holds for 3D polyominos with minimum area.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Winston C. Yang
• Keywords: Bumped-body Polyform, COMBINATORICS 2006, Finite Set, Polyform