Geometry of Semilinear Embeddings

Relations to Graphs and Codes

Nonfiction, Science & Nature, Mathematics, Combinatorics, Graphic Methods
Cover of the book Geometry of Semilinear Embeddings by Mark Pankov, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mark Pankov ISBN: 9789814651097
Publisher: World Scientific Publishing Company Publication: May 28, 2015
Imprint: WSPC Language: English
Author: Mark Pankov
ISBN: 9789814651097
Publisher: World Scientific Publishing Company
Publication: May 28, 2015
Imprint: WSPC
Language: English

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.

Contents:

  • Semilinear Mappings:

    • Division Rings and Their Homomorphisms
    • Vector Spaces Over Division Rings
    • Semilinear Mappings
    • Semilinear Embeddings
    • Mappings of Grassmannians Induced by Semilinear Embeddings
    • Kreuzer's Example
    • Duality
    • Characterization of Strong Semilinear Embeddings
  • Projective Geometry and Linear Codes:

    • Projective Spaces
    • Fundamental Theorem of Projective Geometry
    • Proof of Theorem 1.2
    • m-independent Subsets in Projective Spaces
    • PGL-subsets
    • Generalized MacWilliams Theorem
    • Linear Codes
  • Isometric Embeddings of Grassmann Graphs:

    • Graph Theory
    • Elementary Properties of Grassmann Graphs
    • Embeddings
    • Isometric Embeddings
    • Proof of Theorem 3.1
    • Equivalence of Isometric Embeddings
    • Linearly Rigid Isometric Embeddings
    • Remarks on Non-isometric Embeddings
    • Some Results Related to Chow's Theorem
    • Huang's Theorem
  • Johnson Graph in Grassmann Graph:

    • Johnson Graph
    • Isometric Embeddings of Johnson Graphs in Grassmann Graphs
    • Proof of Theorem 4.2
    • Classification Problem and Relations to Linear Codes
    • Characterizations of Apartments in Building Grassmannians
  • Characterization of Isometric Embeddings:

    • Main Result, Corollaries and Remarks
    • Characterization of Distance
    • Connectedness of the Apartment Graph
    • Intersections of J(n, k)-subsets of Different Types
    • Proof of Theorem 5.1
  • Semilinear Mappings of Exterior Powers:

    • Exterior Powers
    • Grassmannians
    • Grassmann Codes

Readership: Graduate students and researchers interested in the field of semilinear embeddings.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

Contents:

Readership: Graduate students and researchers interested in the field of semilinear embeddings.

More books from World Scientific Publishing Company

Cover of the book The Langevin Equation by Mark Pankov
Cover of the book Adventures in Quantumland by Mark Pankov
Cover of the book Black Holes by Mark Pankov
Cover of the book Advanced Mathematical and Computational Tools in Metrology and Testing XI by Mark Pankov
Cover of the book Photochemical Processes in Continuous-Flow Reactors by Mark Pankov
Cover of the book Design Techniques for Integrated CMOS Class-D Audio Amplifiers by Mark Pankov
Cover of the book Crop Biotechnology by Mark Pankov
Cover of the book Sports Nation by Mark Pankov
Cover of the book Advances in Atmospheric Chemistry by Mark Pankov
Cover of the book Quantum Mechanics by Mark Pankov
Cover of the book Univer-Cities: Strategic Implications for Asia by Mark Pankov
Cover of the book Valuation in a World of CVA, DVA, and FVA by Mark Pankov
Cover of the book Next Generation Experiments to Measure the Neutron Lifetime by Mark Pankov
Cover of the book statsNotes by Mark Pankov
Cover of the book Building Proofs by Mark Pankov
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy