Concerning regular triple systems

Resolving Triple Systems into Regular Configurations

A λ − Triple System(v), or a λ–TS(V,B), is a pair (V, B) where V is a set and B is a subset of the 3-subsets of V so that every pair is in exactly λ elements of B. A regular configuration on p points with regularity ρ on l blocks is a pair (P,L) where L is a collection of 3-subsets of a (usually small) set P so that every p in P is in exactly ρ elements of L, and |L| = l. The Pasch configuratio...

Concerning Connected and Regular Point Sets

In this paper an extension will be given of a theorem of the author'sf which states that if A and B are any two points of a continuous curve M, and K denotes the set of all those points of M which separate} A and B in M, then K+A+B is a closed set of points. I t will be shown that if A and B are any two points of any connected and regular (connected im kleinen) point set M, and K denotes the se...

A Note concerning Completely Regular Gyspaces1

Two results concerning distance-regular directed graphs

The study of distance-regular directed graphs can be reduced to that of short distance-regular directed graphs. We consider the eigenspaces of the intersection matrix of a short distance-regular directed graph and show that nearly all the eigenvalues are nonreal. Next we show that a nontrivial short distance-regular directed graph is primitive.

Embedding Steiner triple systems in hexagon triple systems