English

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.

Keywords

Cite

@article{arxiv.math/0408396,
  title  = {Collinear Points in Permutations},
  author = {J. Cooper and J. Solymosi},
  journal= {arXiv preprint arXiv:math/0408396},
  year   = {2007}
}

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7 pages, 0 figures