Collinear Points in Permutations

Details Collinear Points in Permutations Collinear Points in Permutations

2004-08-29

arxiv.org/abs/math/0408396v1

Mathematics

Combinatorics

7 pages, 0 figures

Scientific paper

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.

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