Combinatorial Study of Dellac Configurations and $q$-Extended Normalized Median Genocchi Numbers

Ange Bigeni

Abstract


In two recent papers, Feigin proved that the Poincaré polynomials of the degenerate flag varieties have a combinatorial interpretation through Dellac configurations, and related them to the $q$-extended normalized median Genocchi numbers $\bar{c}_n(q)$ introduced by Han and Zeng, mainly by geometric considerations. In this paper, we give combinatorial proofs of these results by constructing statistic-preserving bijections between Dellac configurations and two other combinatorial models of $\bar{c}_n(q)$.

Keywords


Genocchi numbers; Dumont permutations; Dellac configurations; Dellac histories

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