{"product_id":"combinatorics-of-spreads-and-parallelisms-9781439819463","title":"Combinatorics of Spreads and Parallelisms","description":"\u003cp\u003e • Author(s): Norman Johnson\u003cbr\u003e • Publisher: Taylor \u0026amp; Francis\u003cbr\u003e • Publisher Imprint: CRC Press\u003cbr\u003e • BISAC: Geometry - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCombinatorics of Spreads and Parallelisms\u003c\/strong\u003e 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.\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cp\u003eAlong with the author's other three books (\u003cem\u003eSubplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes\u003c\/em\u003e), 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.\u003c\/p\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Hardcover","offer_id":45235542229143,"sku":"9781439819463","price":6701.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781439819463.webp?v=1769210068","url":"https:\/\/atlanticbooks.com\/products\/combinatorics-of-spreads-and-parallelisms-9781439819463","provider":"Atlantic Books","version":"1.0","type":"link"}