An Introduction to Incidence Geometry

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Sprache: Englisch

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Beschreibung

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs.

This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.

Zusammenfassung

Provides one of the few in the area of Incidence Geometry which discusses several families of point-line geometries at the same time

Includes the graph theory necessary for the study of certain point-line geometries

Shows the connections between these various point-line geometries

Inhaltsverzeichnis

1.Introductory notions.- 2.Some classes of point-line geometries.- 3.Strongly regular and distance-regular graphs.- 4.Projective spaces.- 5.Generalized polygons.- 6.Near polygons.- 7.Polar spaces.- 8.Dual polar spaces.- 9.Designs.

Details

Erscheinungsjahr:	2016
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	384
Reihe:	Frontiers in Mathematics
Inhalt:	xii 372 S.
ISBN-13:	9783319438108
ISBN-10:	3319438107
Sprache:	Englisch
Herstellernummer:	978-3-319-43810-8
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	De Bruyn, Bart
Auflage:	1st ed. 2016
Hersteller:	Springer International Publishing Frontiers in Mathematics
Maße:	240 x 168 x 21 mm
Von/Mit:	Bart De Bruyn
Erscheinungsdatum:	17.11.2016
Gewicht:	0,643 kg