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Combinatorics of k-shapes and Genocchi numbers

Abstract : In this paper we present a work in progress on a conjectural new combinatorial model for the Genocchi numbers. This new model called irreducible k-shapes has a strong algebraic background in the theory of symmetric functions and leads to seemingly new features on the theory of Genocchi numbers. In particular, the natural q-analogue coming from the degree of symmetric functions seems to be unknown so far.
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https://hal.inria.fr/hal-01215049
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Florent Hivert, Olivier Mallet. Combinatorics of k-shapes and Genocchi numbers. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.493-504, ⟨10.46298/dmtcs.2928⟩. ⟨hal-01215049⟩

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