Finite Geometries and Combinatorics

This is a collection of 35 articles on covering topics such as finite projective spaces, generalised polygons, strongly regular graphs, diagram geometries and polar spaces.

F. de Clerck (Edited by), J. Hirschfeld (Edited by)

9780521448505, Cambridge University Press

Paperback, published 21 October 1993

424 pages
22.9 x 15.2 x 2.3 cm, 0.598 kg

Finite geometry and combinatorics is the art of counting any phenomena that can be described by a diagram. Everyday life is full of applications; from telephones to compact disc players, from the transmission of confidential information to the codes on any item on supermarket shelves. This is a collection of thirty-five articles on covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries and polar spaces. Included here are articles from many of the leading practitioners in the field including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results and the growing use of computer algebra packages in this area is also demonstrated.

1. Generalized hexagons and BLT-sets L. Bader and G. Lunardon
2. Orthogonally divergent spreads of Hermitian curves R. D. Baker, G. L. Ebert, G. Korchmáros, and T.Szönyi
3. Lifts of nuclei in finite projective spaces A. Blokhuis and F. Mazzocca
4. Large minimal blocking sets, strong representative systems, and partial unitals A. Blokhuis and K. Metsch
5. The complement of a geometric hyperplane in a generalized polygon is usually connected A. E. Brouwer
6. Locally co-Heawood graphs A. E. Brouwer, D. G. Fon-der-Flaass, and S. V. Shpectorov
7. A theorem of Parmentier characterizing projective spaces by polarities F. Buekenhout
8. Geometries with diagrams LP* F. Buekenhout and O. H. King
9. Remarks on finite generalized hexagons and octagons with a point transitive automorphism group F. Buekenhout and H. van Maldeghem
10. Block-transitive t- designs, II: large t P. J. Cameron and C. E. Praeger
11. Generalized Fischer spaces H. Cuypers
12. Ovoids and windows in finite generalized hexagons V. de Smet and H. van Maldeghem
13. Flag transitive L.C2 geometries D. Ghinelli
14. On nonics, ovals and codes in Desarguesian planes of even order D. G. Glynn
15. Orbits of arcs in projective spaces C. E. Gordon
16. There exists no (76,21,2,7) regular graph W. Haemers
17. Group arcs of prime power order on cubic curves J. W. P. Hirschfeld and J. Voloch
18. Planar Singer groups with even order multiplier groups C. Y. Ho
19. On a footnote of Tits concerning Dn-geometries C. Huybrechts
20. The structure of the central units of a commutative plane V. Jha and G. P. Wene
21. Partially sharp subsets of PGL(n,q) N. L. Johnson
22. Partial ovoids and generalized hexagons G. Lunardon
23. A census of known flag-transitive extended grids T. Meixner and A. Pasini
24. Root lattice constructions of ovoids G. E. Moorhouse
25. Coxeter groups in Coxeter groups B. Mühlherr
26. A local characterization of the graphs of alternating forms A. Munemasa and S. V. Shpectorov
27. A local characterization of the graphs of alternating forms and the graphs of quadratic forms over GF(2) A. Munemasa, D. V. Pasechnik, and S. V. Shpectorov
28. On some locally 3-transposition graphs D. V. Pasechnik
29. Coherent configurations derived from quasiregular points in generalized quadrangles S. E. Payne
30. On Veldkamp spaces E. E. Shult
31. The Lyons group has no distance transitive representation L. H. Soicher
32. Intersection of arcs and normal rational curves in spaces of odd characteristic L. Storme and T. Szönyi
33. Flocks and partial flocks of the quadratic cone in PG(3,q) J. A. Thas, C. Herssens, and F. de Clerck
34. Some extended generalized hexagons J. van Bon
35. Nuclei in finite non-Desarguesian projective planes F. Wettl.

Subject Areas: Combinatorics & graph theory [PBV]