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On tetrahedrally closed line systems and a generalization of the Haemers-Roos inequality

Bart De Bruyn (UGent)
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Abstract
We generalize the well-known Haemers-Roos inequality for generalized hexagons of order (s, t) to arbitrary near hexagons S with an order. The proof is based on the fact that a certain matrix associated with S is idempotent. The fact that this matrix is idempotent has some consequences for tetrahedrally closed line systems in Euclidean spaces. One of the early theorems relating these line systems with near hexagons is known to contain an essential error. We fix this gap here in the special case for geometries having an order. (C) 2020 Elsevier Inc. All rights reserved.
Keywords
HEXAGONS, POINTS, Line systems, Tetrahedrally closed, Near polygon, Generalized polygon

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

MLA
De Bruyn, Bart. “On Tetrahedrally Closed Line Systems and a Generalization of the Haemers-Roos Inequality.” LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 600, 2020, pp. 130–47, doi:10.1016/j.laa.2020.04.018.
APA
De Bruyn, B. (2020). On tetrahedrally closed line systems and a generalization of the Haemers-Roos inequality. LINEAR ALGEBRA AND ITS APPLICATIONS, 600, 130–147. https://doi.org/10.1016/j.laa.2020.04.018
Chicago author-date
De Bruyn, Bart. 2020. “On Tetrahedrally Closed Line Systems and a Generalization of the Haemers-Roos Inequality.” LINEAR ALGEBRA AND ITS APPLICATIONS 600: 130–47. https://doi.org/10.1016/j.laa.2020.04.018.
Chicago author-date (all authors)
De Bruyn, Bart. 2020. “On Tetrahedrally Closed Line Systems and a Generalization of the Haemers-Roos Inequality.” LINEAR ALGEBRA AND ITS APPLICATIONS 600: 130–147. doi:10.1016/j.laa.2020.04.018.
Vancouver
1.
De Bruyn B. On tetrahedrally closed line systems and a generalization of the Haemers-Roos inequality. LINEAR ALGEBRA AND ITS APPLICATIONS. 2020;600:130–47.
IEEE
[1]
B. De Bruyn, “On tetrahedrally closed line systems and a generalization of the Haemers-Roos inequality,” LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 600, pp. 130–147, 2020.
@article{8669549,
  abstract     = {{We generalize the well-known Haemers-Roos inequality for generalized hexagons of order (s, t) to arbitrary near hexagons S with an order. The proof is based on the fact that a certain matrix associated with S is idempotent. The fact that this matrix is idempotent has some consequences for tetrahedrally closed line systems in Euclidean spaces. One of the early theorems relating these line systems with near hexagons is known to contain an essential error. We fix this gap here in the special case for geometries having an order. (C) 2020 Elsevier Inc. All rights reserved.}},
  author       = {{De Bruyn, Bart}},
  issn         = {{0024-3795}},
  journal      = {{LINEAR ALGEBRA AND ITS APPLICATIONS}},
  keywords     = {{HEXAGONS,POINTS,Line systems,Tetrahedrally closed,Near polygon,Generalized polygon}},
  language     = {{eng}},
  pages        = {{130--147}},
  title        = {{On tetrahedrally closed line systems and a generalization of the Haemers-Roos inequality}},
  url          = {{http://dx.doi.org/10.1016/j.laa.2020.04.018}},
  volume       = {{600}},
  year         = {{2020}},
}

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