Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers
Abstract
In two recent papers (Mathematical Research Letters,18(6):1163--1178,2011 and European J. Combin.,33(8):1913--1918,2012), Feigin proved that the Poincar\'e polynomials of the degenerate flag varieties have a combinatorial interpretation through the Dellac configurations, and related them to the q-extended normalized median Genocchi numbers cn(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 the Dellac configurations and two other combinatorial models of cn(q).
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