Collinear Points in Permutations
Combinatorics
2007-05-23 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0408396,
title = {Collinear Points in Permutations},
author = {J. Cooper and J. Solymosi},
journal= {arXiv preprint arXiv:math/0408396},
year = {2007}
}
Comments
7 pages, 0 figures