Balanced tournament designs and related topics
This is an excellent review paper on the topic of Balanced Tournament Designs. A balanced tournament design of order n, BTD(n), is an \(n\times (2n-1)\) array defined on a set of 2n elements V such that (1) each cell of the array contains a pair of distinct elements from V, (2) every pair of distinct elements from V is contained in some cell, (3) each element is contained in each column, and (4) no element is contained in more than 2 cells of each row. As is well known by now, the existence of such designs has been completely settled. All the crucial theorems are reviewed and various extensions and generalizations are presented. Close connections with other combinatorial systems are also pointed out, such as Room squares, Kotzig factorizations in graph theory, resolvable balanced incomplete block designs, Kirkman squares, etc. All in all, highly recommended reading for researchers in combinatorial designs.
scientific article; zbMATH DE number 4116544
scientific article