Many observed spatial point patterns contain points placed roughly on line segments. Point patterns exhibiting such structures can be found for example in archaeology (locations of bronze age graves in Denmark) and geography (locations of mountain tops). We consider a particular class of point processes whose realizations contain such linear structures. Such a point process is constructed seque...

A A-linked design is an abstract system of v 'points' and b lines' such that every two points are joined by exactly A lines. A partial classification is given of those extremal examples with b = v, and necessary and sufficient conditions are proved for them to be of each of the only two non-trivial types known, namely square BIBDs and point-complemented square BIBDs. For each A > 1 the number o...

The nonexistence of a symmetric configuration with 33 points and line size 6 is established by means of a point-by-point backtrack search and clique searching. An equivalent result is that there exists no 6-regular bipartite graph with 66 vertices and girth 6. Combining with earlier results, it is now known that a symmetric configuration with line size 6 exists if and only if the number of poin...

Given n points in the plane, a covering path is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least n/2 segments, and n − 1 straight line segments obviously suffice even if the covering path is required to be noncrossing. We show that every set of n points in the plane admits a (possibly self-crossing) covering path consisting of ...

Rahilly [10] described a construction that relates any Hadamard design H on 4m−1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m...