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

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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Cited literature [13 references]

https://hal.inria.fr/hal-01207575
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dmAT0141.pdf
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### Citation

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, ⟨10.46298/dmtcs.2415⟩. ⟨hal-01207575⟩

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