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Abstract
My talk is a survey on finite translation generalized quadrangles. To each translation generalized quadrangle of order (s, t), with s not equal 1 not equal t, there corresponds a set O(n, m, q) of q(m) + 1 (n - 1)-dimensional subspaces of the projective space PG(2n+m-1, q) satisfying (i) every three subspaces generate a PG (3n - 1, q) and (ii) for every such subspace pi there is a subspace PG(n + m - 1, q) containing pi and having empty intersection with the other elements of O(n, m, q). Conversely, every such O(n, m, q) defines a finite translation generalized quadrangle. For each known example of O(n, m, q) we have m is an element of {n, 2n}, and for q even there are no other examples. Many papers were written on the case m = 2n. Here emphasis is on the case m = n, and besides interesting and useful old results several new theorems are stated.
Keywords
ORDER S, HERMITIAN SURFACE, Q-EVEN, OVOIDS, SPACES, S(2), SETS

Citation

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Chicago
Thas, Joseph. 2009. “Finite Translation Generalized Quadrangles.” In Statistical Science and Interdisciplinary Research, ed. NSN Sastry, TSSRK Rao, M Delampady, and B Rajeev, 8:223–246. Singapore, Singapore: World Scientific Publications.
APA
Thas, J. (2009). Finite translation generalized quadrangles. In N. Sastry, T. Rao, M. Delampady, & B. Rajeev (Eds.), Statistical Science and Interdisciplinary Research (Vol. 8, pp. 223–246). Presented at the Conference on Perspectives in Mathematical Sciences, Singapore, Singapore: World Scientific Publications.
Vancouver
1.
Thas J. Finite translation generalized quadrangles. In: Sastry N, Rao T, Delampady M, Rajeev B, editors. Statistical Science and Interdisciplinary Research. Singapore, Singapore: World Scientific Publications; 2009. p. 223–46.
MLA
Thas, Joseph. “Finite Translation Generalized Quadrangles.” Statistical Science and Interdisciplinary Research. Ed. NSN Sastry et al. Vol. 8. Singapore, Singapore: World Scientific Publications, 2009. 223–246. Print.
@inproceedings{980020,
  abstract     = {My talk is a survey on finite translation generalized quadrangles. To each translation generalized quadrangle of order (s, t), with s not equal 1 not equal t, there corresponds a set O(n, m, q) of q(m) + 1 (n - 1)-dimensional subspaces of the projective space PG(2n+m-1, q) satisfying (i) every three subspaces generate a PG (3n - 1, q) and (ii) for every such subspace pi there is a subspace PG(n + m - 1, q) containing pi and having empty intersection with the other elements of O(n, m, q). Conversely, every such O(n, m, q) defines a finite translation generalized quadrangle. For each known example of O(n, m, q) we have m is an element of \{n, 2n\}, and for q even there are no other examples. Many papers were written on the case m = 2n. Here emphasis is on the case m = n, and besides interesting and useful old results several new theorems are stated.},
  author       = {Thas, Joseph},
  booktitle    = {Statistical Science and Interdisciplinary Research},
  editor       = {Sastry, NSN and Rao, TSSRK and Delampady, M and Rajeev, B},
  isbn         = {9789814273640},
  language     = {eng},
  location     = {Bangalore, India},
  pages        = {223--246},
  publisher    = {World Scientific Publications},
  title        = {Finite translation generalized quadrangles},
  volume       = {8},
  year         = {2009},
}

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