Skip to main content
Springer Nature Link
Log in

An extremal problem for Graham-Rothschild parameter words

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

This paper exposes connections between the theory of Möbius functions and extremal problems, extending ideas of Frankl and Pach [8]. Extremal results concerning the trace of objects in geometric lattices and Graham—Rothschild parameter posets are proved, covering previous results due to Sauer [16] and Perles and Shelah [17].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Aigner,Combinatorial Theory, Springer Verlag, New York (1979).

    Google Scholar 

  2. N. Alon, On the density of sets of vectors,Disc. Math.,46 (1983), 199–202.

    Google Scholar 

  3. N. Alon andV. D. Milman, Embedding ofl k ∞ in finite dimensional Banach spaces,Israel J. of Math.,45 (1983), 265–280.

    Google Scholar 

  4. A. Benzait andB. Voigt, A combinatorial interpretation of +1/k!Δktn,Disc. Math.,73 (1989), 27–35.

    Google Scholar 

  5. M. Deza andP. Frankl, On the vector space of O-configurations,Combinatorica,2 (1982), 341–345.

    Google Scholar 

  6. M. Deza, P. Frankl andN. M. Singhi, On functions of strengtht, Combinatorica,3 (1983), 331–339.

    Google Scholar 

  7. P. Frankl, On the trace of finite sets,JCT(A),34 (1983), 41–45.

    Google Scholar 

  8. P. Frankl andJ. Pach, On the number of sets in a nullt-design,Europ. J. Comb.,4 (1983), 21–23.

    Google Scholar 

  9. P. Frankl andN. M. Singhi, Linear dependencies among subsets of a finite set,Europ. J. Comb.,4 (1983), 313–318.

    Google Scholar 

  10. R. L. Graham, S.-Y. R. Li andW.-C. W. Li, On the structure oft-designs,SIAM J. Alg Disc. Meth.,1 (1980), 8–14.

    Google Scholar 

  11. R. L. Graham andB. L. Rothschild, Ramsey's theorem forn-parameter sets,Trans. AMS,159 (1971), 257–292.

    Google Scholar 

  12. J. E. Graver andW. B. Jurkat, The module structure of integral designs,JCT(A),15 (1973), 75–90.

    Google Scholar 

  13. M. Karpovsky andV. D. Milman, Coordinate density of sets of vectors,Disc. Math.,24 (1978), 177–184.

    Google Scholar 

  14. H. J.Prömel and B.Voigt, Graham—Rothschild parameter sets,to appear in: The Mathematics of Ramsey Theory, ed. by J. Něsětril, V. Rödl.

  15. G. C. Rota, On the foundations of Combinatorial Theory: I. Theory of Möbius functions,Z. f. Wahrscheinlichkeitstheorie,2 (1964), 340–368.

    Google Scholar 

  16. N. Sauer, On the density of families of sets,JCT(A),13 (1972), 145–147.

    Google Scholar 

  17. S. Shelah, A combinatorial problem; stability and order for models and theories in infinitary languages,Pacific J. of Math.,41 (1972), 247–261.

    Google Scholar 

  18. L. Weisner, Abstract theory of inversion of finite series,Trans. AMS,38 (1935), 474–484.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 8640, D-4800, Bielefeld I, West-Germany

    H. Lefmann

Authors
  1. H. Lefmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lefmann, H. An extremal problem for Graham-Rothschild parameter words. Combinatorica 9, 153–160 (1989). https://doi.org/10.1007/BF02124677

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02124677

AMS subject classification (1980)

Search

Navigation