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 35 articles on covering topics such as finite projective spaces, generalised 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…mehr
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 35 articles on covering topics such as finite projective spaces, generalised 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.
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.
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