Skip to main content
SpringerLink
Log in

Small Forbidden Configurations

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

In the present paper we continue the work begun by Sauer, Perles, Shelah and Anstee on forbidden configurations of 0–1 matrices. We give asymptotically exact bounds for all possible 2 × l forbidden submatrices and almost all 3 × l ones. These bounds are improvements of the general bounds, or else new constructions show that the general bound is best possible. It is interesting to note that up to the present state of our knowledge every forbidden configuration results in polynomial asymptotic.

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

Access this article

Log in via an institution

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. Anstee, R.P.: General forbidden configuration theorems. J. Comb. Theory Ser. A 40, 108–124 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Anstee, R.P., Füredi, Z.: Forbidden Submatrices. Discrete Math. 62, 225–243 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  3. Anstee R.P.: A forbidden configuration theorem of Alon. J. Comb. Theory Ser. A 47, 16–27 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Anstee R.P.: Some Problems Concerning Forbidden Configurations. J. Austr. Math. Soc. (in press)

  5. Anstee R.P.: Forbidden Configurations: Induction and Linear Algebra (preprint)

  6. Frankl, P.: On the trace of finite sets. J. Comb. Theory Ser. A 34, 41–45 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  7. Frankl, P., Füredi, Z., Pach, J.: Bounding One-Way Differences. Graphs and Combinatorics 3, 341–347. 266 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  8. Füredi Z.: Private communication.

  9. Sauer, N.: On the density of families of sets. J. Comb. Theory Ser. A 13, 145–147 (1973)

    Article  MathSciNet  Google Scholar 

  10. Shelah, S.: A combinatorial problem: Stability and order for models and theories in infinitary languages. Pac. J. Math. 4, 247–261 (1972)

    Article  Google Scholar 

Download references

Author information

Author notes

  1. Attila Sali

    Present address: Math. Inst. of Hung. Acad. Sci., P.o.b. 127, H-1364, Budapest, Hungary

Authors and Affiliations

  1. Mathematics Department, The University of British Columbia, Vancouver, B.C., Canada, V6T 1Y4

    Richard Anstee

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Jerrold R. Griggs

  3. Department of Mathematics, Kyushu University, Faculty of Science, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812, Japan

    Attila Sali

Authors
  1. Richard Anstee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerrold R. Griggs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Attila Sali
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anstee, R., Griggs, J.R. & Sali, A. Small Forbidden Configurations. Graphs and Combinatorics 13, 97–118 (1997). https://doi.org/10.1007/BF03352989

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03352989

Keywords

Search

Navigation