The evolution of dioecy, the condition of having populations with distinct male (with only staminate flowers) and female (with only carpellate flowers) plants, has been widely studied in angiosperms. A key to understanding the evolution of dioecy is to understand the genetic mechanisms responsible for the differentiation of male versus female plants. This research builds on the existing knowledge of sexual system evolution, by investigating the genomic architecture of sex determination in the genus Thalictrum (the meadow-rues, Ranunculaceae). The goal was to build a foundation for determining whether similar or different genetic mechanisms were utilized in the two independent origins of dioecy within the genus. Thalictrum is a particularly interesting genus for the study of sex determination because flower developmental studies have suggested that it may use a homeotic mechanism to achieve unisexuality: numerous similar primordia in the center of each flower develop as either stamens or free carpels depending on the sex-determining genetic regions. Using Illumina short read sequencing from pooled same sex individuals of T. dasycarpum and T. dioicum, representatives of each dioecious clade, I developed a k-mer based pipeline to make inferences about the architecture of sex determination and evaluate the likelihood that similar or distinct genomic regions determine sex in each clade. I found evidence of XY sex determination systems in both T. dasycarpum and T. dioicum, yet it seems the two species use different genetic mechanisms.