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Pseudo-embeddings and pseudo-hyperplanes

Bart De Bruyn (UGent)
(2013) ADVANCES IN GEOMETRY. 13(1). p.71-95
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Abstract
We generalize some known results regarding hyperplanes and projective embeddings of point-line geometries with three points per line to geometries with an arbitrary but finite number of points on each line. In order to generalize these results, we need to introduce the new notions of pseudo-hyperplane, (universal) pseudo-embedding, pseudo-embedding rank and pseudo-generating rank. We prove several connections between these notions and address the problem of the existence of (certain) pseudo-embeddings. We apply this to several classes of point-line geometries. We also determine the pseudo-embedding rank and the pseudo-generating rank of the projective space PG (n,4) and the affine space AG (n,4)
Keywords
pseudo-embedding rank, CON PARTICOLARE RIGUARDO, pseudo-generating rank, DUAL POLAR SPACE, QUELLI CON, GEOMETRIES, Pseudo-hyperplane, (universal) pseudo-embedding, CARATTERI, POLYGONS, SETS

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Citation

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

MLA
De Bruyn, Bart. “Pseudo-Embeddings and Pseudo-Hyperplanes.” ADVANCES IN GEOMETRY, vol. 13, no. 1, 2013, pp. 71–95, doi:10.1515/advgeom-2012-0021.
APA
De Bruyn, B. (2013). Pseudo-embeddings and pseudo-hyperplanes. ADVANCES IN GEOMETRY, 13(1), 71–95. https://doi.org/10.1515/advgeom-2012-0021
Chicago author-date
De Bruyn, Bart. 2013. “Pseudo-Embeddings and Pseudo-Hyperplanes.” ADVANCES IN GEOMETRY 13 (1): 71–95. https://doi.org/10.1515/advgeom-2012-0021.
Chicago author-date (all authors)
De Bruyn, Bart. 2013. “Pseudo-Embeddings and Pseudo-Hyperplanes.” ADVANCES IN GEOMETRY 13 (1): 71–95. doi:10.1515/advgeom-2012-0021.
Vancouver
1.
De Bruyn B. Pseudo-embeddings and pseudo-hyperplanes. ADVANCES IN GEOMETRY. 2013;13(1):71–95.
IEEE
[1]
B. De Bruyn, “Pseudo-embeddings and pseudo-hyperplanes,” ADVANCES IN GEOMETRY, vol. 13, no. 1, pp. 71–95, 2013.
@article{3217947,
  abstract     = {{We generalize some known results regarding hyperplanes and projective embeddings of point-line geometries with three points per line to geometries with an arbitrary but finite number of points on each line. In order to generalize these results, we need to introduce the new notions of pseudo-hyperplane, (universal) pseudo-embedding, pseudo-embedding rank and pseudo-generating rank. We prove several connections between these notions and address the problem of the existence of (certain) pseudo-embeddings. We apply this to several classes of point-line geometries. We also determine the pseudo-embedding rank and the pseudo-generating rank of the projective space PG (n,4) and the affine space AG (n,4)}},
  author       = {{De Bruyn, Bart}},
  issn         = {{1615-715X}},
  journal      = {{ADVANCES IN GEOMETRY}},
  keywords     = {{pseudo-embedding rank,CON PARTICOLARE RIGUARDO,pseudo-generating rank,DUAL POLAR SPACE,QUELLI CON,GEOMETRIES,Pseudo-hyperplane,(universal) pseudo-embedding,CARATTERI,POLYGONS,SETS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{71--95}},
  title        = {{Pseudo-embeddings and pseudo-hyperplanes}},
  url          = {{http://dx.doi.org/10.1515/advgeom-2012-0021}},
  volume       = {{13}},
  year         = {{2013}},
}
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