Combinatorial Properties of Matrices of Zeros and Ones

  • H. J. Ryser
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

This paper is concerned with a matrix A of m rows and n columns, all of whose entries are 0’s and 1’s. Let the sum of row i of A be denoted by ri (i = 1, ... , m) and let the sum of column i of A be denoted by Si (i = 1, ... ,n).

References

  1. 1.
    Marshall Hall, An existence theorem for Latin squares,Bull. Amer. Math. Soc, 51(1945), 387-388.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    P. Hall, On representatives of subsets,J. Lond. Math. Soc, 10(1935), 26-30.MATHCrossRefGoogle Scholar
  3. 3.
    G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities(Cambridge, 1952).Google Scholar
  4. 4.
    Dénes König, Theorie der endlichen und unendlichen Graphen(New York, 1950).Google Scholar
  5. 5.
    R. F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters,Proc. Edinburgh Math. Soc, 21(1903), 144-157.Google Scholar
  6. 6.
    Oystein Ore, Graphs and matching theorems,Duke Math. J., 22(1955), 625-639.CrossRefMathSciNetGoogle Scholar
  7. 7.
    H. J. Ryser, A combinatorial theorem with an application to Latin rectangles,Proc. Amer. Math. Soc, 2(1951), 550-552.Google Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • H. J. Ryser
    • 1
  1. 1.Ohio State UniversityUSA

Personalised recommendations