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On the cylinder conjecture

  • Jan De Beule
  • Jeroen Demeyer
  • Sam Mattheus
  • Péter Sziklai
Article
  • 14 Downloads
Part of the following topical collections:
  1. Special Issue: Finite Geometries

Abstract

In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on the number of non-determined directions, together with an exhaustive computer search for weight functions satisfying particular properties, we prove a relaxed version of the cylinder conjecture for \(p \le 13\). This result also slightly refines a result of Sziklai on point sets in \(\mathrm {AG}(3,p)\).

Keywords

Cylinder conjecture Polynomial method Affine space 

Mathematics Subject Classification

05B25 51D20 

Notes

Acknowledgements

The authors acknowledge Aart Blokhuis and Klaus Metsch for the fruitful discussions on the combinatorial part (Sect. 2).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselBelgium
  2. 2.Department of MathematicsGhent UniversityGentBelgium
  3. 3.Department of Computer ScienceEötvös Loránd UniversityBudapestHungary

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