Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- On maximum size anti-Pasch sets of triples
- Some simple 7–designs
- Inscribed bundles, Veronese surfaces and caps
- Embedding partial geometries in Steiner designs
- Finite geometry after Aschbacher's Theorem: PGL(n, q) from a Kleinian viewpoint
- The Hermitian function field arising from a cyclic arc in a Galois plane
- Intercalates everywhere
- Difference sets: an update
- Computational results for the known biplanes of order 9
- A survey of small embeddings for partial cycle systems
- Rosa triple systems
- Searching for spreads and packings
- A note on Buekenhout-Metz unitals
- Elation generalized quadrangles of order (q2, q)
- Uniform parallelisms of PG(3, 3)
- Double-fives and partial spreads in PG(5, 2)
- Rank three geometries with simplicial residues
- Generalized quadrangles and the Axiom of Veblen
- Talks
- Participants
Embedding partial geometries in Steiner designs
Published online by Cambridge University Press: 04 November 2009
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- On maximum size anti-Pasch sets of triples
- Some simple 7–designs
- Inscribed bundles, Veronese surfaces and caps
- Embedding partial geometries in Steiner designs
- Finite geometry after Aschbacher's Theorem: PGL(n, q) from a Kleinian viewpoint
- The Hermitian function field arising from a cyclic arc in a Galois plane
- Intercalates everywhere
- Difference sets: an update
- Computational results for the known biplanes of order 9
- A survey of small embeddings for partial cycle systems
- Rosa triple systems
- Searching for spreads and packings
- A note on Buekenhout-Metz unitals
- Elation generalized quadrangles of order (q2, q)
- Uniform parallelisms of PG(3, 3)
- Double-fives and partial spreads in PG(5, 2)
- Rank three geometries with simplicial residues
- Generalized quadrangles and the Axiom of Veblen
- Talks
- Participants
Summary
Abstract
We consider the following problem: given a partial geometry with v points and k points on a line, can one add to the line set a set of k-subsets of points such that the extended family of k-subsets is a 2-(v, k;, 1) design (or a Steiner system S(2, k, v)). We give some necessary conditions for such embeddings and several examples. One of these is an embedding of the partial geometry PQ+(7,2) into a 2-(120,8,1) design.
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- Information
- Geometry, Combinatorial Designs and Related Structures , pp. 33 - 42Publisher: Cambridge University PressPrint publication year: 1997
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