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Combinatorics of Spreads and Parallelisms (Hardcover)
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Combinatorics of Spreads and Parallelisms (Hardcover)
Series: Chapman & Hall Pure and Applied Mathematics
Expected to ship within 12 - 19 working days
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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.
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