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κ-arcs and partial flocks

Leo Storme (UGent) and Joseph Thas (UGent)
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Abstract
Using the relationship between partial flocks of the quadratic cone K in PG(3, q), q even, and arcs in the plane PG(2, q), new results on partial flocks and short proofs for known theorems on translation generalized quadrangles of order (q(2), q) and on ovoids in PC(3, q) are obtained. It is shown that large partial flocks of K containing approximately q conics, q even, are always extendable to a flock, which improves a result by Payne and Thas. Then new and short proofs are given for a theorem of Johnson on translation generalized quadrangles and a theorem of Glynn on ovoids.
Keywords
GENERALIZED QUADRANGLES

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Citation

Please use this url to cite or link to this publication:

Chicago
Storme, Leo, and Joseph Thas. 1995. “Κ-arcs and Partial Flocks.” Linear Algebra and Its Applications 226-228: 33–45.
APA
Storme, L., & Thas, J. (1995). κ-arcs and partial flocks. LINEAR ALGEBRA AND ITS APPLICATIONS, 226-228, 33–45.
Vancouver
1.
Storme L, Thas J. κ-arcs and partial flocks. LINEAR ALGEBRA AND ITS APPLICATIONS. 1995;226-228:33–45.
MLA
Storme, Leo, and Joseph Thas. “Κ-arcs and Partial Flocks.” LINEAR ALGEBRA AND ITS APPLICATIONS 226-228 (1995): 33–45. Print.
@article{194992,
  abstract     = {Using the relationship between partial flocks of the quadratic cone K in PG(3, q), q even, and arcs in the plane PG(2, q), new results on partial flocks and short proofs for known theorems on translation generalized quadrangles of order (q(2), q) and on ovoids in PC(3, q) are obtained. It is shown that large partial flocks of K containing approximately q conics, q even, are always extendable to a flock, which improves a result by Payne and Thas. Then new and short proofs are given for a theorem of Johnson on translation generalized quadrangles and a theorem of Glynn on ovoids.},
  author       = {Storme, Leo and Thas, Joseph},
  issn         = {0024-3795},
  journal      = {LINEAR ALGEBRA AND ITS APPLICATIONS},
  keyword      = {GENERALIZED QUADRANGLES},
  language     = {eng},
  pages        = {33--45},
  title        = {\ensuremath{\kappa}-arcs and partial flocks},
  url          = {http://dx.doi.org/10.1016/0024-3795(94)00231-2},
  volume       = {226-228},
  year         = {1995},
}

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