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{\bf Winston C. Yang}
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{\bf Adding Layers to Bumped-Body Polyforms with Minimum Perimeter Preserves Minimum Perimeter}
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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.
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