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Dual embeddings of dense near polygons

Bart De Bruyn (UGent)
(2012) ARS COMBINATORIA. 103. p.33-54
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Abstract
Let e: S -> Sigma be a full polarized projective embedding of a dense near polygon S, i.e., for every point p of S, the set H(p) of points at non-maximal distance from p is mapped by e into a hyperplane Pi(p) of Sigma. We show that if every line of S is incident with precisely three points or if S satisfies a certain property (P(de)) then the map p bar right arrow Pi p defines a full polarized embedding e* (the so-called dual embedding of e) of S into a subspace of the dual Sigma* of Sigma. This generalizes a result of [6] where it was shown that every embedding of a thick dual polar space has a dual embedding. We determine which known dense near polygons satisfy property (P(de)). This allows us to conclude that every full polarized embedding of a known dense near polygon has a dual embedding.
Keywords
polarized embedding, GEOMETRIES, hyperplane, dual embedding, near polygon

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Citation

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

MLA
De Bruyn, Bart. “Dual Embeddings of Dense near Polygons.” ARS COMBINATORIA, vol. 103, 2012, pp. 33–54.
APA
De Bruyn, B. (2012). Dual embeddings of dense near polygons. ARS COMBINATORIA, 103, 33–54.
Chicago author-date
De Bruyn, Bart. 2012. “Dual Embeddings of Dense near Polygons.” ARS COMBINATORIA 103: 33–54.
Chicago author-date (all authors)
De Bruyn, Bart. 2012. “Dual Embeddings of Dense near Polygons.” ARS COMBINATORIA 103: 33–54.
Vancouver
1.
De Bruyn B. Dual embeddings of dense near polygons. ARS COMBINATORIA. 2012;103:33–54.
IEEE
[1]
B. De Bruyn, “Dual embeddings of dense near polygons,” ARS COMBINATORIA, vol. 103, pp. 33–54, 2012.
@article{3101091,
  abstract     = {{Let e: S -> Sigma be a full polarized projective embedding of a dense near polygon S, i.e., for every point p of S, the set H(p) of points at non-maximal distance from p is mapped by e into a hyperplane Pi(p) of Sigma. We show that if every line of S is incident with precisely three points or if S satisfies a certain property (P(de)) then the map p bar right arrow Pi p defines a full polarized embedding e* (the so-called dual embedding of e) of S into a subspace of the dual Sigma* of Sigma. This generalizes a result of [6] where it was shown that every embedding of a thick dual polar space has a dual embedding. We determine which known dense near polygons satisfy property (P(de)). This allows us to conclude that every full polarized embedding of a known dense near polygon has a dual embedding.}},
  author       = {{De Bruyn, Bart}},
  issn         = {{0381-7032}},
  journal      = {{ARS COMBINATORIA}},
  keywords     = {{polarized embedding,GEOMETRIES,hyperplane,dual embedding,near polygon}},
  language     = {{eng}},
  pages        = {{33--54}},
  title        = {{Dual embeddings of dense near polygons}},
  url          = {{http://cage.ugent.be/geometry/Files/280/dual_emb.pdf}},
  volume       = {{103}},
  year         = {{2012}},
}

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