Finite translation generalized quadrangles
- Author
- Joseph Thas (UGent)
- Organization
- 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
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-980020
- 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}, }