دانلود کتاب Geometry of Semilinear Embeddings: Relations to Graphs and Codes

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Content: Preface
1. Semilinear mappings
1.1 Division rings and their homomorphisms
1.2 Vector spaces over division rings
1.3 Semilinear mappings
1.4 Semilinear embeddings
1.5 Mappings of Grassmannians induced by semilinear embeddings
1.6 Kreuzer\'s example
1.7 Duality
1.8 Characterization of strong semilinear embeddings
2. Projective Geometry and linear codes
2.1 Projective spaces
2.2 Fundamental Theorem of Projective Geometry
2.3 Proof of Theorem 1.2
2.4 m-independent subsets in projective spaces
2.5 PGL-subsets
2.6 Generalized MacWilliams theorem
2.7 Linear codes 3. Isometric embeddings of Grassmann graphs3.1 Graph theory
3.2 Elementary properties of Grassmann graphs
3.3 Embeddings
3.4 Isometric embeddings
3.5 Proof of Theorem 3.1
3.6 Equivalence of isometric embeddings
3.7 Linearly rigid isometric embeddings
3.8 Remarks on non-isometric embeddings
3.9 Some results related to Chow\'s theorem
3.10 Huang\'s theorem
3.10.1 Proof of Theorem 3.2 for n = 2k
3.10.2 Proof of Theorem 3.2 for n 6= 2k
4. Johnson graph in Grassmann graph
4.1 Johnson graph
4.2 Isometric embeddings of Johnson graphs in Grassmann graphs
4.3 Proof of Theorem 4.2 4.4 Classification problem and relations to linear codes4.5 Characterizations of apartments in building Grassmannians
5. Characterization of isometric embeddings
5.1 Main result, corollaries and remarks
5.2 Characterization of distance
5.3 Connectedness of the apartment graph
5.4 Intersections of J(n, k)-subsets of different types
5.5 Proof of Theorem 5.1
6. Semilinear mappings of exterior powers
6.1 Exterior powers
6.2 Grassmannians
6.3 Grassmann codes
Bibliography
Index