Collinear Points in Permutations |
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| Authors: | Joshua N Cooper József Solymosi |
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| Institution: | (1) Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, USA;(2) Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada |
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| Abstract: | Consider the following problem: how many collinear triples of points must a transversal of
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.Received August 29, 2004 |
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| Keywords: | 51E15 11T99 |
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