Minimum-Perimeter Lattice Animals and the Constant-Isomer Conjecture

Abstract

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.