A Construction for Large Sets of Pairwise Disjoint Extended Directed Triple Systems

摘要

Starting with two famous recreational problems, Euler's problem of the Thirty six officers and Kirkman's schoolgirl problem, and stimulated by the needs of computer science, digital communication, modern business management, the subject of design theory has grown into a large branch of combinatorial mathematics. Large set of design is an important topic of design theory, which has some valuable applications to experimental design, coding theory and so on. Though the topic has acquired numerous great advances in recent years, due to its difficulty, the progress is not more than expected. An extended directed triple system is one of oriented designs, It was studied first by Huang and Yaon, By now the question about the large sets of extended directed triple system has not been discussed. In this paper, We give the concept of large sets of extended directed triple system and a recursive construction for large sets of extended directed triple system.