On subset-sum-distinct sequences

  • Jaegug Bae
Part of the Progress in Mathematics book series (PM, volume 138)

Abstract

We use Tomić’s inequality to show some interesting properties of subset-sum-distinct sequences including an elementary proof of a theorem of Steele, Hanson, and Stenger. Also, we comment on a theorem of L. Moser.

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References

  1. [1]
    N. Alon, J. H. Spencer, and P. Erdös, The Probabilistic Method, John Wiley & Sons, Inc., New York, 1992.MATHGoogle Scholar
  2. [2]
    J. H. Conway and R. K. Guy, Solution of a problem of P. Erdös, Colloquium Mathematicum 20 (1969), 307.Google Scholar
  3. [3]
    N. D. Elkies, An improved lower bound on the greatest element of a sumdistinct set of fixed order, Journal of Combinatorial Theory, Series A 41 (1986), 89–94.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Erdös, Problems and results in additive number theory, Colloque sur la Théorie des Nombres (1955), Bruxelles, 127–137.Google Scholar
  5. [5]
    P. Erdös, Some of my favorite unsolved problems, A tribute to Paul Erdös (A. Baker, B. Bollobás and A. Hajnal, eds.), Cambridge University Press, Cambridge, 1990, pp. 467–478.Google Scholar
  6. [6]
    P. Erdös and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L’Enseignement Mathématique 28 (1980), Université de Genève;, L’Enseignement Mathématique, Geneva.Google Scholar
  7. [7]
    R. K. Guy, Unsolved Problems in Intuitive Mathematics, Vol.I, Number Theory, Springer-Verlag, New York, 1994.Google Scholar
  8. [8]
    R. K. Guy, Sets of integers whose subsets have distinct sums, Annals of Discrete Mathematics 12 (1982), 141–154.MATHMathSciNetGoogle Scholar
  9. [9]
    F. Hanson, J. M. Steele, and F. Stenger, Distinct sums over subsets, Proc. Amer. Math. Soc. 66 (Sep. 1977), no. 1, 179–180.MATHMathSciNetGoogle Scholar
  10. [10]
    W. F. Lunnon, Integer sets with distinct subset-sums, Mathematics of Computation 50 (Jan. 1988), no. 181, 297–320.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    G. Pólya, Remark on Weyl’s note “Inequalities between the two kinds of eigenvalues of a linear transformation”, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 49–51.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    P. Smith, Problem E2526, Amer. Math. Monthly 82 (1975), 300; 83 (1976), 484; 88 (1981), 538–539.CrossRefMathSciNetGoogle Scholar
  13. [13]
    M. Tomić, Gauss’ theorem on the centroid and its application, Bull. Soc. Math. Phys. Serbie 1 (1949), no. 1, 31–40. (Serbian)MATHGoogle Scholar
  14. [14]
    H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 408–411.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Jaegug Bae
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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