Combinatorica

, Volume 9, Issue 4, pp 393–395

A nowhere-zero point in linear mappings

  • N. Alon
  • M. Tarsi
Note

Abstract

We state the following conjecture and prove it for the case whereq is a proper prime power:

Let A be a nonsingular n by n matrix over the finite field GFqq≧4, then there exists a vector x in (GFq)n such that both x and Ax have no zero component.

AMS subject classifications (1980)

05 B 35 05 B 25 12 C 05 

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References

  1. [1]
    N.Alon, E. E.Bergmann, D.Coppersmith and A. M.Odlyzko, Balancing sets of vectors,IEEE Transactions on Information Theory, in press.Google Scholar
  2. [2]
    A. E. Brouwer andA. Schrijver, The blocking number of an affine space,J. Combinatorial Theory, Ser. A24 (1978), 251–253.Google Scholar
  3. [3]
    F. Jaeger, Problem presented in the 6th Hungar. Comb. Coll., Eger, Hungary1981, and:Finite and Infinite Sets (eds.: Hajnal, A., Lovász, L., Sós, V. T.). North Holland, Amsterdam, 1982 II, 879.Google Scholar
  4. [4]
    D. J. A. Welsh,Matroid Theory, Academic Press, San Francisco, 1976.Google Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • N. Alon
    • 1
  • M. Tarsi
    • 1
  1. 1.School of Mathematical Sciences Sackler Faculty of Exact SciencesTel Aviv UniversityRamat Aviv Tel AvivIsrael

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