Geodesic
Calculating the dimension of the universal embedding of the symplectic dual polar space using languages
Carlos Segovia1 ; Monika Winklmeier2
1IMUNAM-Oaxaca
2Universidad de Los Andes
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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The main result of this paper is the construction of a bijection of the set of words in so-called standard order of length $n$ formed by four different letters and the set $\mathcal{N}^n$ of all subspaces of a fixed $n$-dimensional maximal isotropic subspace of the $2n$-dimensional symplectic space $V$ over $\mathbb{F}_2$ which are not maximal in a certain sense. Since the number of different words in standard order is known, this gives an alternative proof for the formula of the dimension of the universal embedding of a symplectic dual polar space $\mathcal{G}_n$. Along the way, we give formulas for the number of all $n$- and $(n-1)$-dimensional totally isotropic subspaces of $V$.
DOI : 10.37236/9754
Classification : 05B25, 51A50, 68R15, 51A45
Mots-clés : totally isotropic subspaces, projective geometry

Carlos Segovia  1   ; Monika Winklmeier  2

1 IMUNAM-Oaxaca
2 Universidad de Los Andes 
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     title = {Calculating the dimension of the universal embedding of the symplectic dual polar space using languages},
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Carlos Segovia; Monika Winklmeier. Calculating the dimension of the universal embedding of the symplectic dual polar space using languages. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9754

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