Bijections for Directed Animals on Infinite Families of Lattices

Abstract

Bousquet-Melou and Conwayin [1] found algebraic equations for the area generating function of directed animals on an infinite family of regular, non-planar, two-dimensional lattices by using equivalences with hard particle models. We give in this paper a bijective proof of their results which is a generalization of Viennot's heaps of pieces [10,12]. Based on this proof we get exacte numeration formulas for the number of configurations with area n which could not be deduced directly from the algebraic equation. Moreover, we give an extension of these results to another infinite family of lattices.