Decomposing the blocks of a Steiner triple system of order 4v-3 into partial parallel classes of size v-1
Date of Award
Open Access Master's Report
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Melissa S. Keranen
Committee Member 1
Donald L. Kreher
Committee Member 2
Timothy C. Havens
In this report we present a summary and our new results on finding partial parallel classes of uniform size of Steiner triple systems, STS(v). We show several results for STS(4v - 3), where v = 3 mod 12 and v = 9 mod 12. In Chapter 1 we provide background knowledge and introduce the problem. In Chapter 2 we discuss some important known results to the problem, introduce the needed ingredients, and explain the methodology of the construction. Finally, in Chapter 3, we conclude with a summary and discuss possibilities for future work.
Tollefson, Leah C., "Decomposing the blocks of a Steiner triple system of order 4v-3 into partial parallel classes of size v-1", Open Access Master's Report, Michigan Technological University, 2015.