On a Generalization of Rédei’s Theorem

In 1970 Rédei and Megyesi proved that a set of p points in AG(2,p), p prime, is a line, or it determines at least \( \frac{{p + 3}} {2} \) directions. In ’81 Lovász and Schrijver characterized the case of equality. Here we prove that the number of determined directions cannot be between \( \frac{{p + 5}} {2} \) and \( 2\frac{{p - 1}} {3} \). The upper bound obtained is one less than the smallest known example.

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Correspondence to András Gács.

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Gács, A. On a Generalization of Rédei’s Theorem. Combinatorica 23, 585–598 (2003). https://doi.org/10.1007/s00493-003-0035-y

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Mathematics Subject Classification (2000):

  • 51E15