Rettangoli latini e “transversal designs” con parallelismo

A complete system of mutually orthogonal latin rectangles is defined here as in [1] and [2]. A resolvable transversal design (RTD). as defined here, is a transversal design in the sense of [3], provided there is λ=1 and there exists a parallelism (i.e. an equivalence relation among the blocks) satisfying the Euelidean axiom. We prove the following tlieorems:Theorem 1. Foe evenr ordered pair (m, n) of integers (m≥n≥2), such that each prime divisor of m is not less than n, there exists (and tliere is actually obtained) at least one complete system of mutually orthogonal m x n latin rectangles.Theorem 2. Every resolvable transversal design, RTD (m, n) with m≥n≥2, defines a complete system of mutually orthogonal m x n latin rectangles; and conversely.