Movable (n4) Configurations

) Configurations Exist for Almost All N –– an Update

It has been known since the late 1800’s that connected (n3) configurations exist if an only if n ≥ 9. However, the analogous question concerning connected (n4) configurations was not considered till very recently ([2], [3]). This is probably due to the fact that –– except for one paper early in the 20 century [5], there has been no mention in the literature of (n4) configurations till 1990 ([4]...

On topological and geometric $(19_4)$ configurations

An (nk) configuration is a set of n points and n lines such that each point lies on k lines while each line contains k points. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. The existence and enumeration of (nk) configurations for a given k has been subject to active research...

Quasi-configurations: building blocks for point-line configurations

We study generalized point – line configurations and their properties in the projective plane. These generalized configurations can serve as building blocks for (n4) configurations. In this way, we construct (374) and (434) configurations. The existence problem of finding such configurations for the remaining cases (224), (234), and (264) remains open.

Estimating Response Time for Auxiliary Memory Configurations with Multiple Movable-Head Disk Modules

Connected (n 4 ) Configurations Exist for Almost All N

An (n4) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely four of the lines, and each line contains precisely four 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 configurati...