A Lower Bound on the Growth Constant of Polyaboloes on the Tetrakis Lattice.

A “lattice animal” is an edge-connected set of cells on a lattice. In this paper we consider the Tetrakis lattice, and provide the first lower bound on \(\lambda _\tau \), the growth constant of polyaboloes (animals on this lattice), proving that \(\lambda _\tau \ge 2.4345\). The proof of the bound is based on a concatenation argument and on calculus manipulations. If we also rely on an unproven assumption, which is, however, supported by empirical data, we obtain the conditional slightly-better lower bound 2.4635.