Finite geometry and combinatorial applications

by Ball, Simeon, (Simeon Michael)

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Title Statements

Full title :Finite geometry and combinatorial applications / Simeon Ball, Universitat Politècnica de Catalunya, Barcelona.

Edition Statements

Publication Date:©2015

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:©2015

The Physical Object

Description:xii, 285 pages : : illustrations ; : 24 cm.

Edition Identifiers

ISBN:9781107107991, 1107107997, 9781107518438, 1107518431
oclc:ocn906171742
LC Classification:QA167.2
Dewey Decimal:516/.11

1.Fields -- 1.1.Rings and fields -- 1.2.Field automorphisms -- 1.3.The multiplicative group of a finite field -- 1.4.Exercises -- 2.Vector spaces -- 2.1.Vector spaces and subspaces -- 2.2.Linear maps and linear forms -- 2.3.Determinants -- 2.4.Quotient spaces -- 2.5.Exercises -- 3.Forms -- 3.1.[MARC+76]-Sesquilinear forms -- 3.2.Classification of reflexive forms -- 3.3.Alternating forms -- 3.4.Hermitian forms -- 3.5.Symmetric forms -- 3.6.Quadratic forms -- 3.7.Exercises -- 4.Geometries -- 4.1.Projective spaces -- 4.2.Polar spaces -- 4.3.Quotient geometries -- 4.5.Generalised polygons -- 4.6.Plucker coordinates -- 4.7.Polarities -- 4.8.Ovoids -- 4.9.Exercises -- 5.Combinatorial applications -- 5.1.Groups -- 5.2.Finite analogues of structures in real space -- 5.3.Codes -- 5.4.Graphs -- 5.5.Designs -- 5.6.Permutation polynomials -- 5.7.Exercises -- 6.The forbidden subgraph problem -- 6.1.The Erdos -- Stone theorem -- 6.2.Even cycles -- 6.3.Complete bipartite graphs -- 6.4.Graphs containing no K2,s -- 6.5.A probabilistic construction of graphs containing no Kt,s -- 6.6.Graphs containing no K3,3 -- 6.7.The norm graph -- 6.8.Graphs containing no K5,5 -- 6.9.Exercises -- 7.MDS codes -- …