Abstract
A lattice animal is a connected set of cells on a lattice. The perimeter of a lattice animal A consists of all the cells that do not belong to A, but that have a least one neighboring cell of A. We consider minimal-perimeter lattice animals, that is, animals whose periemeter is minimal for all animals of the same area, and provide a set of conditions that are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result for polyhexes (animals on the two-dimensional hexagonal lattice).
Cite
CITATION STYLE
Barequet, G., & Ben-Shachar, G. (2020). On Minimal-Perimeter Lattice Animals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12118 LNCS, pp. 519–531). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-61792-9_41
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