Dellac构型与q-扩展的归一化中值Genocchi数的组合研究
Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers
摘要：
在最近的两篇论文（\textit{Mathematical Research Letters,18(6):1163--1178,2011}和\textit{European J. Combin.,33(8):1913--1918,2012}）中，Feigin证明了退化旗簇的庞加莱多项式通过Dellac配置具有组合解释，并将它们与Han和Zeng引入的$q$ -扩展的归一化中值Genocchi数$\bar{c}_n(q)$联系起来，主要是通过几何考虑。本文通过构造Dellac构型与$\bar{c}_n(q)$的其它两个组合模型之间的保投影双射，给出了这些结果的组合证明.
英文摘要：
In two recent papers (\textit{Mathematical Research Letters,18(6):1163--1178,2011} and \textit{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 $\bar{c}_n(q)$ 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 the Dellac configurations and two other combinatorial models of $\bar{c}_n(q)$.
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