# Which (n 4 ) Configurations Exist ?

@inproceedings{GrnbaumWhich4, title={Which (n 4 ) Configurations Exist ?}, 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. While the study of (n 3) configurations goes back more than a century, very little has been written about the geometric (n k) configurations for k ≥ 4. (See [1], [2], [3], [4], which seems to be a complete list of published references on this topic.) It is well known that there exist (n k…

## 6 Citations

) Configurations Exist for Almost All N –– an Update

- Mathematics

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…

Connected ( n k ) configurations exist for almost all n

- Mathematics
- 2021

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…

New bounds on the existence of $(n_{5})$ and $(n_{6})$ configurations: the Gr\"{u}nbaum Calculus revisited

- Mathematics
- 2022

. The “Gr¨unbaum Incidence Calculus” is the common name of a collection of operations introduced by Branko Gr¨unbaum to produce new ( n 4 ) conﬁgurations from various input conﬁgurations. In a…

Even Astral Configurations

- MathematicsElectron. J. Comb.
- 2004

This paper completes the classification of all even astral configurations and defines an astral configuration configuration whereq and k are both even.

A Characterization of Astral (n4) Configurations

- Mathematics, PhysicsDiscret. Comput. Geom.
- 2001

A conjecture of Branko Grünbaum concerning what astral (n4) configurations exist is shown to be true.

Movable (n4) Configurations

- MathematicsElectron. J. Comb.
- 2006

A tantalum capacitor comprising a cylindrical body and an axial tantalum anode wire. This wire is first folded and then soldered to an anode connection wire roughly parallel to a cathode connection…

## References

SHOWING 1-4 OF 4 REFERENCES

Astral (n 4 ) Configurations

- Mathematics

A family of n points and n (straight) lines in the Euclidean plane is said to be an (n 4) configuration provided each point is on four of the lines and each line contains four of the points. A…

The Real Configuration (214)

- Mathematics
- 1990

The configuration (21 4 ), considered by Klein, Burnside, Coxeter and others, is realized by points and lines in the real projective plane

Astral (n k ) configurations

- Geombinatorics
- 1993

Sur les configurations planes n 4

- Bull Cl. Sci. Acad. Roy. Belg
- 1913