Geodesic
Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1032
Classification : 05B50, 05B45
Mots-clés : grid, polyominos 
@article{10_37236_1032,
     author = {Winston C. Yang},
     title = {Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1032},
     zbl = {1080.05017},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1032/}
}
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Winston C. Yang. Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perim\-eter. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1032

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