## Tournament Schedules Using Combinatorial Design Theory

Student thesis: Master Thesis and HD Thesis

• Christian Serup Ravn Thorsen
4. term, Mathematics, Master (Master Programme)
This thesis considers organization of tournament schedules with certain requirements on symmetry from a combinatorial perspective. To describe this, block designs are introduced along with several properties and results. Most important of these are Fisher's inequality and the Bruck-Ryser-Chowla theorem, both of which excludes the existence of certain designs. Fisher's inequality holds for any design, while the Bruck-Ryser-Chowla theorem holds for symmetric designs.

Resolvable designs and difference systems are introduced to construct a tournament of 2n teams where each team meet once. Firstly, it is constructed such that there are 2n-2 breaks in the pattern of home and away games and it is then extended to include a second half with venues interchanged where there are 6n-6 breaks and no consecutive breaks.

Secondly, a flaw in this construction is described, and to remove this flaw, a construction where there are no teams x and y that both play team z immediately after playing team w, is presented.
Language English 8 Jan 2021 42
ID: 398822919