In 1986 G.X. Viennot published "Heaps of pieces, I : Basic definitions and combinatorial lemmas" where he developed the theory of heaps of pieces, from the abstract: a geometric interpretation of Cartier-Foata's commutation monoid. This theory unifies and simplifies many other works in Combinatorics : bijective proofs in matrix algebra (MacMahon Master theorem, inversion matrix formula, Jacobi identity, Cayley-Hamilton theorem), combinatorial theory for general (formal) orthogonal polynomials, reciprocal of Rogers-Ramanujan identities, graph theory (matching and chromatic polynomials).

In the references the subsequent articles "Heaps of pieces, 4 and 5" are listed as "in preparation" where the applications of the theory to solving the directed animal problem and statistical physics are supposed to be developed. I know that these parts of the theory have appeared in literature but I am sort of puzzled as to why the series of papers was not continued (searching for Heaps of pieces II or III or IV doesn't give results). Is there any survey of the full theory somewhere else?

Also, since I didn't feel like asking this in a separate question, is there any paper that proves classical theorems of dimers (Kasteleyn's theorem, Aztec diamond etc.) using Viennot's theory?