Combinatorics of Spreads and Parallelisms

Norman Johnson

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English

CRC Press
14 October 2024

Discrete mathematics; Algebra; Geometry; Combinatorics & graph theory

Series: Chapman & Hall Pure and Applied Mathematics

Combinatorics of Spreads and Parallelisms covers all known finite and infinite parallelisms as well as the planes comprising them. It also presents a complete analysis of general spreads and partitions of vector spaces that provide groups enabling the construction of subgeometry partitions of projective spaces.

The book describes general partitions of finite and infinite vector spaces, including Sperner spaces, focal-spreads, and their associated geometries. Since retraction groups provide quasi-subgeometry and subgeometry partitions of projective spaces, the author thoroughly discusses subgeometry partitions and their construction methods. He also features focal-spreads as partitions of vector spaces by subspaces. In addition to presenting many new examples of finite and infinite parallelisms, the book shows that doubly transitive or transitive t-parallelisms cannot exist unless the parallelism is a line parallelism.

Along with the author’s other three books (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes), this text forms a solid, comprehensive account of the complete theory of the geometries that are connected with translation planes in intricate ways. It explores how to construct interesting parallelisms and how general spreads of vector spaces are used to study and construct subgeometry partitions of projective spaces.

By: Norman Johnson
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.242kg
ISBN: 9781032917849
ISBN 10: 1032917849
Series: Chapman & Hall Pure and Applied Mathematics
Pages: 674
Publication Date: 14 October 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Partitions of Vector Spaces. Subgeometry Partitions. Subplane Covered Nets and Baer Groups. Flocks and Related Geometries. Derivable Geometries. Constructions of Parallelisms. Parallelism-Inducing Groups. Coset Switching. Transitivity. Appendices. Bibliography. Index.

Norman L. Johnson is a professor in the Department of Mathematics at the University of Iowa.