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

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 c̄n(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 c̄n(q).