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

Ange Bigeni

paper

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

arXiv:1402.1383

Abstract

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 $G_{2 k}$ .