Mendelsohn directed triple systems

The spectrum of rotational directed triple systems and rotational Mendelsohn triple systems

Necessary and sufficient conditions for the existence of k-rotational directed triple systems and k-rotational Mendelsohn triple systems are derived.

Pure Latin directed triple systems

It is well-known that, given a Steiner triple system, a quasigroup can be formed by defining an operation · by the identities x · x = x and x ·y = z where z is the third point in the block containing the pair {x, y}. The same is true for a Mendelsohn triple system where the pair (x, y) is considered to be ordered. But it is not true in general for directed triple systems. However directed tripl...

Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1 Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with λ = 1. Also, we obtain the spectrum for cyclic such systems.

Large sets of disjoint directed and Mendelsohn packing triple systems on 6k+5 points

Directed Triple Systems

Directed triple systems are an example of block designs on directed graphs. A block design on a directed graph can be defined as follows. Let G be a directed graph of k vertices which contain no loops. Let S be a set of v elements. A collection of k-subsets of S with an assignment of the elements of each k-subset to the vertices of G is called a block design on G of order v if the following is ...