On the size of a blocking set inPG(2,p)

Combinatorica volume 14, pages111–114(1994)Cite this article

Abstract

We show that the size of a non-trivial blocking set in the Desarguesian projective planePG(2,p), wherep is prime, is at least 3(p+1)/2. This settles a 25 year old conjecture of J. di Paola.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. [1]

    A. Blokhuis, andA. E. Brouwer: Blocking sets in desarguesian projective planes,Bull. London Math. Soc. 18 (1986), 132–134.

    Google Scholar 

  2. [2]

    A. Blokhuis, A. E. Brouwer, andT. Szőnyi: The number of directions determined by a functionf on a finite field,manuscript.

  3. [3]

    A. E. Brouwer, andA. Schrijver: The blocking number of an affine space,J. Combin. Theory (A) 24 (1978), 251–253.

    Google Scholar 

  4. [4]

    A. A. Bruen: Blocking sets in finite projective planes,SIAM J. Appl. Math. 21 (1971), 380–392.

    Google Scholar 

  5. [5]

    A. A. Bruen, andR. Silverman: Arcs and blocking sets II,Europ. J. Combin. 8 (1987), 351–356.

    Google Scholar 

  6. [6]

    J. Di Paola: On minimum blocking coalitions in small projective plane games,SIAM J. Appl. Math. 17 (1969), 378–392.

    Google Scholar 

  7. [7]

    R. Jamison: Covering finite fields with cosets of subspaces,J. Combin. Theory (A) 22 (1977), 253–266.

    Google Scholar 

  8. [8]

    L. Lovász, andA. Schrijver: Remarks on a theorem of Rédei,Studia Scient. Math. Hungar. 16 (1981), 449–454.

    Google Scholar 

  9. [9]

    L. Rédei: Lückenhafte Polynome über endlichen Körpern,Birkhäuser Verlag, Basel (1970).

    Google Scholar 

Download references

Author information

Affiliations

  1. Tech. University Eindhoven, P. O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Aart Blokhuis

Authors
  1. Aart Blokhuis
    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

Blokhuis, A. On the size of a blocking set inPG(2,p). Combinatorica 14, 111–114 (1994). https://doi.org/10.1007/BF01305953

Download citation

AMS subject classification code (1991)

  • 05 B 25