Finite Geometries and Combinatorics

doi:10.1017/CBO9780511526336

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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Preface
pp ix-x
- By Albrecht Beutelspacher, Francis Buekenhout, Frank De Clerck, Jean Doyen, James W. P. Hirschfeld, Joseph A. Thas
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Introduction
pp 1-4
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Generalized hexagons and BLT-sets
pp 5-16
- By L. Bader, G. Lunardon, The authors are members of G.N.S.A.G.A. of C.N.R. and have partial financial support by Italian M.U.R.S.T.
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Orthogonally divergent spreads of Hermitian curves
pp 17-30
- By R. D. Baker, G. L. Ebert, G. Korchmáros, T. Szönyi
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Lifts of nuclei in finite projective spaces
pp 31-36
- By A. Blokhuis, F. Mazzocca, This author gratefully acknowledges for their support the Italian M.U.R.S.T. and C.N.R.(G.N.S.A.G.A.).
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Large minimal blocking sets, strong representative systems, and partial unitals
pp 37-52
- By A. Blokhuis, K. Metsch
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The complement of a geometric hyperplane in a generalized polygon is usually connected
pp 53-58
- By A. E. Brouwer
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Locally co-Heawood graphs
pp 59-68
- By A. E. Brouwer, D. G. Fon-der-Flaass, S. V. Shpectorov
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A theorem of Parmentier characterizing projective spaces by polarities
pp 69-72
- By F. Buekenhout
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Geometries with diagram (diagram omitted)
pp 73-88
- By F. Buekenhout, O.H. King
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Remarks on finite generalized hexagons and octagons with a point-transitive automorphism group
pp 89-102
- By F. Buekenhout, H. Van Maldeghem, This author is supported by the National Fund for Scientific Research (Belgium).
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Block-transitive t-designs, II: large t
pp 103-120
- By P. J. Cameron, C. E. Praeger
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Generalized Fischer spaces
pp 121-130
- By H. Cuypers
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Ovoids and windows in finite generalized hexagons
pp 131-138
- By V. De Smet, H. Van Maldeghem, Research Associate at the National Fund for Scientific Research (Belgium)
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Flag transitive L.C2 geometries
pp 139-154
- By D. Ghinelli
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On nonics, ovals and codes in Desarguesian planes of even order
pp 155-160
- By David Glynn, This research was supported by a von Humboldt Fellowship at the University of Tubingen, and gratitude is due to a delayed rapido between Florence and Bologna.
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Orbits of arcs in projective spaces
pp 161-174
- By C. Gordon
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There exists no (76,21,2,7) strongly regular graph
pp 175-176
- By W. Haemers
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Group-arcs of prime power order on cubic curves
pp 177-186
- By J. W. P. Hirschfeld, J. F. Voloch
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Planar Singer groups with even order multiplier groups
pp 187-198
- By C. Y. Ho, Partially supported by a grant from NSA.
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On a footnote of Tits concerning Dn-geometries
pp 199-206
- By C. Huybrechts, Aspirant du Fonds National Beige de la Recherche Scientifique
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The structure of the central units of a commutative semifield plane
pp 207-216
- By V. Jha, G. P. Wene
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Partially sharp subsets of PΓL(n, q)
pp 217-232
- By N. L. Johnson
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Partial ovoids and generalized hexagons
pp 233-248
- By G. Lunardon, The author has a partial financial support from the Italian M.U.R.S.T.
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A census of known flag-transitive extended grids
pp 249-268
- By T. Meixner, A. Pasini
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Root lattice constructions of ovoids
pp 269-276
- By G. E. Moorhouse
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Coxeter groups in Coxeter groups
pp 277-288
- By Bernhard Mühlherr
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A local characterization of the graphs of alternating forms
pp 289-302
- By A. Munemasa, This research was completed during this author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical Sciences., S. V. Shpectorov, A part of this research was completed during the visit at University of Technology, Eindhoven.
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