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This paper constructs a bijection between irreducible $k$-shapes and surjective pistols of height $k-1$, which carries the "free $k$-sites" to the fixed points of surjective pistols. The bijection confirms a conjecture of Hivert and Mallet (FPSAC 2011) that the number of irreducible $k$-shape is counted by the Genocchi number $G_{2k}$. On construit une bijection entre les $k$-formes irréductibles et les pistolets surjectifs de hauteur $k-1$ qui envoie les ”$k$-sites libres” sur les points fixes des pistolets. Cette bijection démontre une conjecture de Hivert et Mallet (FPSAC 2011), selon laquelle les $k$-formes irréductibles sont comptées par les nombres de Genocchi $G_{2k}$.

A bijection between irreducible k-shapes and surjective pistols of height $k-1$