• Corpus ID: 15796968

) Configurations Exist for Almost All N –– an Update

@inproceedings{GrnbaumCE,
  title={) Configurations Exist for Almost All N –– an Update},
  author={Branko Gr{\"u}nbaum}
}
An (n k) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely k of the lines, and each line contains precisely k of the points. A configuration is said to be connected if it is possible to reach every point starting from an arbitrary point and stepping to other points only if they are on one of the lines of the configuration. It has been known since the late 1800's that connected (n 3) configurations exist if an only if n ≥ 9… 

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References

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Which (n 4 ) Configurations Exist ?
An (n k) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely k of the lines, and each line contains precisely k of the points.
Connected ( n k ) configurations exist for almost all n
A geometric (nk) configuration is a collection of points and straight lines, typically in the Euclidean plane, so that each line passes through k of the points and each of the points lies on k of the
Polycyclic configurations
The Real Configuration (214)
The configuration (21 4 ), considered by Klein, Burnside, Coxeter and others, is realized by points and lines in the real projective plane
Sur les configurations planes n 4
  • Bull. Cl. Sci. Acad. Roy. Belg
  • 1913