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A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q2$)$

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  • We give a geometric proof of the upper bound of q2n+1$+1$ on the size of partial spreads in the polar space $H(4n+1,$q2$)$. This bound is tight and has already been proved in an algebraic way. Our alternative proof also yields a characterization of the partial spreads of maximum size in $H(4n+1,$q2$)$.
    Mathematics Subject Classification: 05B25, 51E23.


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