From compatible factorization to near-compatible factorization

Abstract

A compatible factorization of order , is an array in which the entries in row form a near-one-factor with focus , and the triples associated with the rows contain no repetitions. In this paper, we aim to amend this compatible factorization so that we can display triples with the minimum repeated triples. Throughout this paper we propose a new type of factorization called near-compatible factorization. First, we present the compatible factorization towards developing a near-compatible factorization. Second, we discuss briefly the necessary and sufficient conditions for the existence of near-compatible factorization. Then, we exemplify the construction for case as a groundwork in developing near-compatible factorization.