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  3. Combinatorial Matrix Classes
  • Cited by 112
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    • Publisher:
      Cambridge University Press
      Publication date:
      April 2010
      August 2006
      ISBN:
      9780511721182
      9780521865654
      DOI:
      https://doi.org/10.1017/CBO9780511721182
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.936kg, 554 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (108)
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (108)
    Information

    Book description

    A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.

    Reviews

    'The treatment is clearly explained, methodical and accurate and includes details of many important algorithms as well as proofs of many important theorems, although some proofs are necessarily omitted … the test is well cross-referenced and thoughtfully written, meaning that it is very accessible. All in all, a treasure trove of results written by an acknowledged master of combinatorial matrix theory.'

    Source: Zentralblatt MATH

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