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Geometry of semilinear embeddings : relations to graphs and codes /
"This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be for...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
[2015]
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Pankov, Mark, |e author. | |
| 245 | 1 | 0 | |a Geometry of semilinear embeddings : |b relations to graphs and codes / |c by Mark Pankov, University of Warmia and Mazury, Poland. |
| 264 | 1 | |a New Jersey : |b World Scientific, |c [2015] | |
| 264 | 4 | |c ©2015 | |
| 300 | |a 1 online resource (xii, 168 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 161-165) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a "This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples."-- |c Provided by publisher | ||
| 590 | |a Knovel |b ACADEMIC - General Engineering & Project Administration | ||
| 650 | 0 | |a Embeddings (Mathematics) | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 0 | |a Grassmann manifolds. | |
| 650 | 6 | |a Plongements (Mathématiques) | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 6 | |a Variétés de Grassmann. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Embeddings (Mathematics) |2 fast |0 (OCoLC)fst00908306 | |
| 650 | 7 | |a Geometry, Algebraic. |2 fast |0 (OCoLC)fst00940902 | |
| 650 | 7 | |a Grassmann manifolds. |2 fast |0 (OCoLC)fst00946825 | |
| 776 | 0 | 8 | |i Print version: |a Pankov, Mark. |t Geometry of semilinear embeddings. |d Singapore ; Hackensack, NJ ; London : World Scientific Publishing Co. Pte. Ltd., [2015] |z 9789814651073 |w (DLC) 2015008649 |w (OCoLC)900028793 |
| 856 | 4 | 0 | |u https://appknovel.uam.elogim.com/kn/resources/kpGSERGC0G/toc |z Texto completo |
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