Geodesic
The maximum size of a partial spread in \(H(4n+1, q^{2})\) is \(q^{2n+1}+1\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We prove that in every finite Hermitian polar space of odd dimension and even maximal dimension $\rho$ of the totally isotropic subspaces, a partial spread has size at most $q^{\rho+1}+1$, where $GF(q^2)$ is the defining field. This bound is tight and is a generalisation of the result of De Beule and Metsch for the case $\rho=2$.
DOI : 10.37236/251
Classification : 51E14, 51E23, 05B25, 05E30
Mots-clés : Hermitian polar space, partial spread, maximum size 
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     author = {Fr\'ed\'eric Vanhove},
     title = {The maximum size of a partial spread in {\(H(4n+1,} q^{2})\) is \(q^{2n+1}+1\)},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/251},
     zbl = {1195.51007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/251/}
}
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Frédéric Vanhove. The maximum size of a partial spread in \(H(4n+1, q^{2})\) is \(q^{2n+1}+1\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/251

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