# Generalized Dellac configurations

@inproceedings{Shigechi2021GeneralizedDC, title={Generalized Dellac configurations}, author={Keiichi Shigechi}, year={2021} }

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.

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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…

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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 $\bar{c}_n(q)$.

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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…

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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…

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