rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Geometry of semilinear embeddings
    sub title: relations to graphs and codes
  name:
    name part: Pankov, Mark
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Knovel (Firm)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nju
    date issued: 2015
    copyright date: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xii, 168 pages)
  abstract: "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."--
  table of contents: 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
  table of contents: 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
  table of contents: 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
  note: by Mark Pankov, University of Warmia and Mazury, Poland.
  note: Includes bibliographical references (pages 161-165) and index.
  subject:
    topic: Embeddings (Mathematics)
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Grassmann manifolds
  subject:
    topic: MATHEMATICS / Geometry / General
  subject:
    topic: Embeddings (Mathematics)
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Grassmann manifolds
  subject:
    topic: Embeddings (Mathematics)
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Grassmann manifolds
  classification: QA564 .P36 2015eb
  classification: 516.3/5
  related item:
    title info:
      title: Geometry of semilinear embeddings
    name:
      name part: Pankov, Mark.
    origin info:
      publisher: Singapore ; Hackensack, NJ ; London : World Scientific Publishing Co. Pte. Ltd., [2015]
    identifier: (DLC) 2015008649
    identifier: (OCoLC)900028793
  identifier: 9789814651080
  identifier: 9814651087
  identifier: 9781680158489
  identifier: 1680158481
  identifier: 9789814651073
  identifier: 9814651079
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 150608
    record change date: 20260609152826.3
    record identifier: in00003833828
    language of cataloging:
      language term: eng