Author
Wolfe, Adam

Year
2005

Advisor
Seress, Acos

Abstract

Abstract of Thesis

Steiner triple systems are known to exist for orders $n \equiv 1,3 \mod 6$. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This thesis resolves the problem of determining the spectrum of orders of anti-mitre Steiner triple systems and gives a proof that the spectrum of orders of 5-sparse Steiner triple systems has arithmetic density 1 as compared to the admissible orders. Several anti-mitre and 5-sparse Steiner triple system constructions are provided as well.

Thesis
Wolfe.Adam.pdf