Finite Geometry and Combinatorics

✍ Scribed by F. de Clerck, J. Hirschfeld

• Publisher: Cambridge University Press
• Year: 1993
• Tongue: English
• Leaves: 423
• Series: London Mathematical Society Lecture Note Series 191
• Category: Library

✦ Synopsis

This is a collection of thirty-five articles, covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries, and polar spaces. Contained 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.

✦ Table of Contents

Contents......Page 6
PREFACE......Page 10
INTRODUCTION......Page 12
Generalized hexagons and BLT-sets......Page 16
Orthogonally divergent spreads of Hermitian curves......Page 28
Lifts of nuclei in finite projective spaces......Page 42
Large minimal blocking sets, strong representative systems,
and partial unitals......Page 48
The complement of a geometric hyperplane in a generalized
polygon is usually connected......Page 64
Locally co-Heawood graphs......Page 70
A theorem of Parmentier characterizing projective spaces by
polarities......Page 80
Geometries with diagram......Page 84
Remarks on finite generalized hexagons and octagons with a
point-transitive automorphism group......Page 100
Block-transitive t-designs, II: large t......Page 114
Generalized Fischer spaces......Page 132
Ovoids and windows in finite generalized hexagons......Page 142
Flag transitive L.C2 geometries......Page 150
On nonics, ovals and codes in Desarguesian planes of even order......Page 166
Orbits of arcs in projective spaces......Page 172
There exists no (76,21,2,7) strongly regular graph......Page 186
Group-arcs of prime power order on cubic curves......Page 188
Planar Singer groups with even order multiplier groups......Page 198
On a footnote of Tits concerning Dn-geometries......Page 210
The structure of the central units of a commutative semifield
plane......Page 218
Partially sharp subsets of PPL(n, q)......Page 228
Partial ovoids and generalized hexagons......Page 244
A census of known flag-transitive extended grids......Page 260
Root lattice constructions of ovoids......Page 280
Coxeter groups in Coxeter groups......Page 288
A local characterization of the graphs of alternating forms......Page 300
A local characterization of the graphs of alternating forms and
the graphs of quadratic forms over GF(2)......Page 314
On some locally 3-transposition graphs......Page 330
Coherent configurations derived from quasiregular points in
generalized quadrangles......Page 338
Veldkamp spaces......Page 352
The Lyons group has no distance-transitive representation......Page 366
Intersection of arcs and normal rational curves in spaces of odd
characteristic......Page 370
Flocks and partial flocks of the quadratic cone in PG(3, q)......Page 390
Some extended generalized hexagons......Page 406
Nuclei in finite non-Desarguesian projective planes......Page 416