On directed-convex polyominoes in a rectangle

We provide bijective proofs for the number of directed-convex polyominoes having a fixed number of rows and columns in two ways: by means of the ECO method, and through a correspondence with the set of 2-colored Grand-Motzkin paths. Resume: Dans cet article, nous donnons des preuves bijectives pour le nombre de polyominos diriges convexes ayant un nombre fixe de lignes et de colonnes, en utilisant la methodologie ECO ainsi qu'une application bijective dans l'ensemble des grands chemins de Motzkin bi-colores.

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