Flocks and ovals

Geometriae Dedicata

Volumn 60, Issue 1, 1996, Pages 17-37

  Cherowitzo, W ^a   Penttila, T ^b   Pinneri, I ^b   Royle, G F ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Flocks; Fundamental quadrangles; Herds; Hyperovals; Ovals; Subiaco q clans; Translation planes

Indexed keywords

EID: 0001919065     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00150865     Document Type: Article

References (25)

1. e, Bull. Belgian Math. Soc., Simon Stevin 1 (1994), 301-328.
2. Bader, L., Lunardon, G. and Thas, J. A.: Derivation of flocks of quadratic cones, Forum Math. 2 (1990), 163-194.
3. Cherowitzo, W.: Hyperovals in Desarguesian planes of even order: an update (preprint).
4. De Clerck, F. and Herssens, C.: Flocks of the quadratic cone in PG(3, q) for q small, The CAGe Report 8 (1992), Computer Algebra Group, The University of Gent, Belgium.
5. Fisher, J. C. and Thas, J. A.: Flocks in PG(3, q), Math. Z. 169 (1979), 1-11.
6. Hall, M. Jr.: Ovals in Desarguesian plane of order l6, Ann. Mat. Pura Appl. 102 (1975), 159-176.
7. Hirschfeld, J. W.: Protective Geometries over Finite Fields, Oxford University Press, Oxford, 1979.
8. 2(q), J. Combin. Theory Ser. A 29 (1980), 212-219.
9. 2,q), Math. Z. 192 (1986), 45-50.
10. Lunelli, L. and See, M.: k-archi completi nei piani proiettivi desarguesiani di rango 8 e 16, Centro di Calcoli Numerici, Politecnico di Milano, 1958.
11. O'Keefe, C. M. and Penttila, T.: Hyperovals in PG(2, 16), European J. Combin. 12 (1991), 51-59.
12. O'Keefe, C. M. and Thas, J. A.: Collineations of some hyperovals (preprint).
13. Payne, S. E.: Generalized quadrangles as group coset geometries, Congr. Numer. 29 (1980), 717-734.
14. Payne, S. E.: A new infinite family of generalized quadrangles, Congr. Numer. 49 (1985), 115-128.
15. Payne, S. E.: An essay on skew translation generalized quadrangles, Geom. Dedicata 32 (1989), 93-118.
16. Payne, S. E.: Collineations of the generalized quadrangles associated with q-clans, Ann. Discrete Math. 52 (1992), 449-461.
17. Payne, S. E.: Collineations of the Subiaco generalized quadrangles, Bull. Belgian Math. Soc., Simon Stevin 1 (1994), 427-438.
18. Payne, S. E., Penttila, T. and Pinneri, I.: Isomorphisms between Subiaco q-clan geometries, Bull. Belgian Math. Soc., Simon Stevin (submitted).
19. Payne, S. E. and Thas, J. A.: Finite Generalized Quadrangles, Research Notes in Mathematics #110, Pitman Publ. Inc., 1984.
20. Penttila, T. and Pinneri, I.: Irregular hyperovals in PG(2, 64), J. Geometry 51 (1994), 89-100.
21. Penttila, T. and Royle, G. F.: Hyperovals in projective planes of small order, J. Geometry (to appear).
22. Penttila, T. and Royle, G. F.: Flocks of quadratic cones in PG(3, q), q small (in preparation).
23. Thas, J. A.: Generalized quadrangles and flocks of cones, European J. Combin. 8 (1987), 441-452.
24. Thas, J. A.: Projective geometry over a finite field, Chapter 8, Handbook of Geometry (preprint).
25. Walker, M.: A class of translation planes, Geom. Dedicata 5 (1976) 133-146.