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 bumpe...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2006-01, Vol.13 (1)
Main Author: Yang, Winston C.
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/1032