Geodesic
On maximal set without parallelograms
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 5-14

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We find upper and lower bounds for the cardinality of the subset in a discrete torus over the field of three elements such that no four different points of it form a nonsingular parallelogram.
Keywords: finite fields, discrete torus, trigonometric sums. 
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     title = {On maximal set without parallelograms},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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E. P. Davletyarova; A. A. Zhukova; A. A. Yudin. On maximal set without parallelograms. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 5-14. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a0/