We define symmetric Dellac configurations as the Dellac configurations that are symmetrical with respect to their centers. The even-length symmetric Dellac config-urations coincide with the Fang-Fourier symplectic Dellac configurations. Symmetric Dellac configurations generate the Poincaré polynomials of (odd or even) symplec-tic or orthogonal versions of degenerate flag varieties. We give several combinatorialinterpretations of the Randrianarivony-Zeng polynomial extension of median Euler numbers in terms of objects that we call extended Dellac configurations. We show that the extended Dellac configurations generate symmetric Dellac configurations. As a consequence, the cardinalities of odd and even symmetric Dellac configurations are respectively given by two sequences (1, 1, 3, 21, 267,…) and (1, 2, 10, 98, 1594, …), de-fined as specializations of polynomial extensions of median Euler numbers.
|Journal||Journal of Integer Sequences|
|State||Published - 2020|
- Dellac configuration
- Flag variety
- Median Euler number