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The isomorphism problem for linear representations and their graphs

(2014) ADVANCES IN GEOMETRY. 14(2). p.353-367
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Abstract
A linear representation T-n(*)(K) of a point set K is a point-line geometry, embedded in a projective space PG (n + 1; q), where K is contained in a hyperplane. We put constraints on K which ensure that every automorphism of T-n(*)(K) is induced by a collineation of the ambient projective space. This allows us to show that, under certain conditions, two linear representations T-n(*)(K) and T-n(*)(K') are isomorphic if and only if the point sets K and K' are PL-equivalent. We also deal with the slightly more general problem of isomorphic incidence graphs of linear representations. In the last part of this paper, we give an explicit description of the group of automorphisms of T-n(*)(K) that are induced by collineations of PG (n + 1; q).
Keywords
incidence graph, Linear representation, automorphism group

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MLA
Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. “The Isomorphism Problem for Linear Representations and Their Graphs.” ADVANCES IN GEOMETRY 14.2 (2014): 353–367. Print.
APA
Cara, P., Rottey, S., & Van de Voorde, G. (2014). The isomorphism problem for linear representations and their graphs. ADVANCES IN GEOMETRY, 14(2), 353–367.
Chicago author-date
Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. 2014. “The Isomorphism Problem for Linear Representations and Their Graphs.” Advances in Geometry 14 (2): 353–367.
Chicago author-date (all authors)
Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. 2014. “The Isomorphism Problem for Linear Representations and Their Graphs.” Advances in Geometry 14 (2): 353–367.
Vancouver
1.
Cara P, Rottey S, Van de Voorde G. The isomorphism problem for linear representations and their graphs. ADVANCES IN GEOMETRY. 2014;14(2):353–67.
IEEE
[1]
P. Cara, S. Rottey, and G. Van de Voorde, “The isomorphism problem for linear representations and their graphs,” ADVANCES IN GEOMETRY, vol. 14, no. 2, pp. 353–367, 2014.
@article{5807930,
  abstract     = {{A linear representation T-n(*)(K) of a point set K is a point-line geometry, embedded in a projective space PG (n + 1; q), where K is contained in a hyperplane. We put constraints on K which ensure that every automorphism of T-n(*)(K) is induced by a collineation of the ambient projective space. This allows us to show that, under certain conditions, two linear representations T-n(*)(K) and T-n(*)(K') are isomorphic if and only if the point sets K and K' are PL-equivalent. We also deal with the slightly more general problem of isomorphic incidence graphs of linear representations. In the last part of this paper, we give an explicit description of the group of automorphisms of T-n(*)(K) that are induced by collineations of PG (n + 1; q).}},
  author       = {{Cara, Philippe and Rottey, Sara and Van de Voorde, Geertrui}},
  issn         = {{1615-715X}},
  journal      = {{ADVANCES IN GEOMETRY}},
  keywords     = {{incidence graph,Linear representation,automorphism group}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{353--367}},
  title        = {{The isomorphism problem for linear representations and their graphs}},
  url          = {{http://dx.doi.org/10.1515/advgeom-2013-0040}},
  volume       = {{14}},
  year         = {{2014}},
}

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