Abstract
We introduce the combinatorial notion of heaps of pieces, which gives a geometric interpretation of the 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). Heaps may bring new light on classical subjects as poset theory. They are related to other fields as Theoretical Computer Science (parallelism) and Statistical Physics (directed animals problem, lattice gas model with hard-core interactions). Complete proofs and definitions are given in sections 2, 3,4,5. Other sections give a summary of possible applications of heaps.
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