Giorgio Faina

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A trivial upper bound on the size k of an arc in an r-net is k ≤ r + 1. It has been known for about 20 years that if the r-net is Desarguesian and has odd order, then the case k = r + 1 cannot occur, and k ≥ r − 1 implies that the arc is contained in a conic. In this paper, we show that actually the same must hold provided that the difference r − k does not(More)
The n-dimensional finite projective space, P G(n, q), admits a cyclic model, in which the set of points of P G(n, q) is identified with the elements of the group Z q n +q n−1 +···+q+1. It was proved by Hall (1974, Math. Centre Tracts, 57, 1–26) that in the cyclic model of P G(2, q), the additive inverse of a line is a conic. The following generalization of(More)