English

Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers

Combinatorics 2014-02-11 v1

Abstract

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 Poincar\'e polynomials of the degenerate flag varieties have a combinatorial interpretation through the Dellac configurations, and related them to the qq-extended normalized median Genocchi numbers cˉn(q)\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 cˉn(q)\bar{c}_n(q).

Keywords

Cite

@article{arxiv.1402.1827,
  title  = {Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers},
  author = {Ange Bigeni},
  journal= {arXiv preprint arXiv:1402.1827},
  year   = {2014}
}