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

Ange Bigeni (1)

1 CTN - Combinatoire, théorie des nombres

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 $G_{2k}$.

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-00942482v2⟩