Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter (Q813922)
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scientific article; zbMATH DE number 5002939
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter |
scientific article; zbMATH DE number 5002939 |
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Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter (English)
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31 January 2006
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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.
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grid
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polyominos
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0.725546658039093
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0.6921747922897339
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0.6801334023475647
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