A nowhere-zero point in linear mappings

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.

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Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild grant.

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Alon, N., Tarsi, M. A nowhere-zero point in linear mappings. Combinatorica 9, 393–395 (1989). https://doi.org/10.1007/BF02125351

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AMS subject classifications (1980)

  • 05 B 35
  • 05 B 25
  • 12 C 05