Directed animals on two-dimensional lattices

Abstract

Previously, directed animals on square and triangular lattices have been enumerated by area, and have been found to have simple generating functions, whilst the hexagonal lattice generating function has not been obtained. Directed animals on several new lattices are enumerated, one class of which is solved exactly. Directed animals by bonds (with and without loops) are also enumerated. In each case an asymptotic growth like n-1/2 mu n is observed and precise estimates for mu are given.