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

Ange Bigeni (1)

1 ICJ - Institut Camille Jordan

We construct a bijection between the irreducible k-shapes and the surjective pistols of height k-1. As a consequence, we solve the main conjecture posed by Hivert and Mallet (Discrete Math. Theor. Comput. Sci. Proc., pages 493-504, Nancy, 2011). In particular, we prove that the irreducible k-shapes are counted by the Genocchi numbers.

Mots clés: Genocchi numbers; Gandhi polynomials; (irreducible) $k$-shapes; surjective pistols

Domaines: Combinatoire [math.CO]

Ange Bigeni. A bijection between the irreducible k-shapes and the surjective pistols of height k-1. 2014. ⟨hal-00942482v1⟩