• Corpus ID: 233033890

Generalized Dellac configurations

  title={Generalized Dellac configurations},
  author={Keiichi Shigechi},
We study combinatorics of two generalizations of Dellac configurations. First, we establish a correspondence between a generalized Dellac configuration with three parameters and a generalized Dumont permutations. Secondly, by relaxing conditions on Dellac configurations, we introduce a generalization which we call Dellac configurations with boundaries. We show several recurrence relations for the Poincaré polynomials of Dellac configurations with boundaries. 

Symmetric Dellac configurations and symplectic/orthogonal flag varieties

Symmetric Dellac configurations

We define symmetric Dellac configurations as the Dellac configurations that are symmetric with respect to their centers. The symmetric Dellac configurations whose lengths are even were previously

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

Combinatorial proofs of the Poincare polynomials of the degenerate flag varieties are given by constructing statistic-preserving bijections between Dellac configurations and two other combinatorial models of $\bar{c}_n(q)$.

Enumerating the symplectic Dellac configurations

Fang and Fourier defined the symplectic Dellac configurations in order to parametrize the torus fixed points of the symplectic degenerated flag varieties, and conjectured that their numbers are the

Torus fixed points in Schubert varieties and normalized median Genocchi numbers

We give a new proof for the fact that the number of torus fixed points for the degenerated flag variety is equal to the normalized median Genocchi number, using the identification with a certain

Further results on the euler and Genocchi numbers

SummaryWe characterize the ordinary generating functions of the Genocchi and median Genocchi numbers as unique solutions of some functional equations and give a direct algebraic proof of several

A q-analog of the Seidel generation of Genocchi numbers

Combinatorial Interpretations of the Kreweras Triangle in Terms of Subset Tuples

It is shown how the combinatorial interpretation of the normalized median Genocchi numbers in terms of multiset tuples is bijectively equivalent to previous models like the normalized Dumont permutations or the Dellac configurations.

Degenerate flag varieties and the median Genocchi numbers

We study the $\bG_a^M$ degenerations $\Fl^a_\la$ of the type $A$ flag varieties $\Fl_\la$. We describe these degenerations explicitly as subvarieties in the products of Grassmanians. We construct