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Manuscripta Mathematica

, Volume 144, Issue 3–4, pp 401–420 | Cite as

Point configurations on the projective line over a finite field

  • Ernst-Ulrich GekelerEmail author
Article
  • 91 Downloads

Abstract

We study n-point configurations in \({\mathbb{P}^1(\mathbb{F}_q)}\) modulo projective equivalence. For n = 4 and 5, a complete classification is given, along with the numbers of such configurations with a given symmetry group. Using Polya’s coloring theorem, we investigate the behavior of the numbers C(n, q) of classes of n-configurations resp. C spec(n, q) of classes with nontrivial symmetry group. Both are described by rational polynomials in q which depend on q modulo \({\lambda(n) = {\rm lcm} \{m \in \mathbb{N} | m \leq n\}}\) .

Mathematics Subject Classifications (2010)

05A15 14N10 11T99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.FR 6.1 Mathematik, Campus E2 4Universität des SaarlandesSaarbrückenGermany

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