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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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Abstract
We give a geometric proof of the upper bound of q(2n+1) + 1 on the size of partial spreads in the polar space H(4n + 1, q(2)). 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, q(2)).
Keywords
partial spreads, Hermitian varieties

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Chicago
Vanhove, Frédéric. 2011. “A Geometric Proof of the Upper Bound on the Size of Partial Spreads in H(4n+1, Q2).” Advances in Mathematics of Communications 5 (2): 157–160.
APA
Vanhove, F. (2011). A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q2). ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 5(2), 157–160.
Vancouver
1.
Vanhove F. A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q2). ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 2011;5(2):157–60.
MLA
Vanhove, Frédéric. “A Geometric Proof of the Upper Bound on the Size of Partial Spreads in H(4n+1, Q2).” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 5.2 (2011): 157–160. Print.
@article{1935440,
  abstract     = {We give a geometric proof of the upper bound of q(2n+1) + 1 on the size of partial spreads in the polar space H(4n + 1, q(2)). 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, q(2)).},
  author       = {Vanhove, Fr{\'e}d{\'e}ric},
  issn         = {1930-5346},
  journal      = {ADVANCES IN MATHEMATICS OF COMMUNICATIONS},
  keyword      = {partial spreads,Hermitian varieties},
  language     = {eng},
  number       = {2},
  pages        = {157--160},
  title        = {A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q{\texttwosuperior})},
  url          = {http://dx.doi.org/10.3934/amc.2011.5.157},
  volume       = {5},
  year         = {2011},
}

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