Minimum-Perimeter Lattice Animals and the Constant-Isomer Conjecture

  • Gill Barequet
  • Gil Ben-Shachar


We consider minimum-perimeter lattice animals, providing a set of conditions which are sufficient for a lattice to have the property that inflating all minimum-perimeter animals of a certain size yields (without repetitions) all minimum-perimeter animals of a new, larger size.  We demonstrate this result on the two-dimensional square and hexagonal lattices.  In addition, we characterize the sizes of minimum-perimeter animals on these lattices that are not created by inflating members of another set of minimum-perimeter animals.


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