2004/08/29 by J. Cooper, Cooper, J., J. Solymosi +1
Mathematics · #11T99 (Secondary) #51E15 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11T99 #msc:51E15
paper · pdf · doi:10.48550/arxiv.math/0408396
7 pages, 0 figures
arxiv created 2004/08/29 · arxiv updated 2009/12/01
Consider the following problem: how many collinear triples of points must a transversal of (Z/nZ)2 have? This question is connected with venerable issues in discrete geometry. We show that the answer, for n prime, is between (n-1)/4 and (n-1)/2, and consider an analogous question for collinear quadruples. We conjecture that the upper bound is the truth and suggest several other interesting problems in this area.