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.

Rettangoli latini e “transversal designs” con parallelismo / Quattrocchi, Pasquale; Pellegrino, Consolato. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - STAMPA. - 28 (n. 2):(1979), pp. 441-449.

Rettangoli latini e “transversal designs” con parallelismo

QUATTROCCHI, Pasquale;PELLEGRINO, Consolato
1979

Abstract

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.
28 (n. 2)
441
449
Rettangoli latini e “transversal designs” con parallelismo / Quattrocchi, Pasquale; Pellegrino, Consolato. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - STAMPA. - 28 (n. 2):(1979), pp. 441-449.
Quattrocchi, Pasquale; Pellegrino, Consolato
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/595017
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