On Latin Triangles

Abstract

Halberstam, Hoffman and Richter introduced the idea of a Latin triangle as an analogue of a Latin square, showed the existence or non-existence of Latin triangles for small orders, and used a multiplication technique to generate triangles of orders $3^n$ and $3^n–1$. We generalize this multiplication theorem and provide a construction of Latin triangles of odd order $n$ for $n$ such that $n+2$ is prime. We also discuss scalar multiplication, orthogonal triangles, and results of computer searches.