Direct constructions of large sets of Kirkman triple systems
The study on the constructions and existence of large sets of Kirkman triple systems can be traced back to 1850, when Cayley and Kirkman independently expounded the solutions for the Kirkman 15 schoolgirls problem. Sylvester further discussed this question for triples systems. Each system can have 455 triples from 15 elements. The problem with large sets of Kirkman triple systems of order 15 was finally solved by \textit{R. H. F. Denniston} [Discrete Math. 9, 229--233 (1974; Zbl 0285.05002)]. During all these decades many questions have been successfully solved, but some questions are open until now. The main purpose of this paper is to study some aspects of relevance and direct constructions of this large sets. For primary definitions refer to the literature in the paper. This paper after reviewing the construction of such structures, aimed at many recursive constructions which will yield several new infinite classes.
scientific article; zbMATH DE number 6696611
scientific article