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

Ange Bigeni 1
1 CTN - Combinatoire, théorie des nombres
ICJ - Institut Camille Jordan [Villeurbanne]
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 $G_{2k}$.
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Ange Bigeni. A bijection between irreducible k-shapes and surjective pistols of height $k-1$. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.465-476. ⟨hal-01207575⟩

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