2014/02/08 by Bigeni, Ange · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1402.1827
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 Poincaré 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).