Introduction and motivations Alternating diagrams Parellolograms polyominoes Generating functions 321-avoiding affine permutations, heaps, and periodic parallelogram polyominoes Riccardo Biagioli (Universit´ e Lyon 1) joint work with Fr´ ed´ eric Jouhet and Philippe Nadeau S´ eminaire Philippe Flajolet 7 d´ ecembre 2017 Riccardo Biagioli (Universit´ e Lyon 1) 321-avoiding affine permutations, heaps, and periodic parallelogram polyominoes