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 noâ€¦ (More)

An orthogonal latin square graph (OLSG) is one in which the vertices are latin squares of the same order and on the same symbols, and two vertices are adjacent if and only if the latin squares areâ€¦ (More)

This paper is concerned with convexity properties of m X n matrices whose entries are non-negative real numbers and whose row and column sums are specified positive numbers. Such matrices make theirâ€¦ (More)

Proof. If c = a o b then c = ha + (1 h) b and since h # 0, h # 1 any two of a, b, c uniquely determine the third. Hence the operation defines a quasi-group and the multiplication table is a Latinâ€¦ (More)

A 3/c-block is a set of 3k points on a real non-singular cubic curve, which are the points of intersection of a real cubic curve and a curve of degree k. It has been proved [3] that 3k1 points on aâ€¦ (More)