Open Access Honors Program Thesis
Dessins d'enfants are bipartite graphs with a cyclic ordering given to the set of edges that meet at each vertex. Merling and Perlis presented a method by which to construct pairs of dessins d'enfants using the permutations induced by the action of a finite group on the cosets of two locally conjugate subgroups of that group. They called these pairs of dessins Gassmann equivalent and investigated some of their properties. First, we discuss several properties of pairs of dessins that imply Gassmann equivalence. Then, using elementwise conjugate subgroups, we introduce and investigate a weaker type of equivalence of dessins, which we refer to as Kronecker equivalence.
Year of Submission
Department of Mathematics
University Honors Designation
A thesis submitted in partial fulfillment of the requirements for the designation University Honors
1 PDF file (25 pages)
©2013 Rachel M. Volkert
Volkert, Rachel M., "Equivalences of Dessins D'Enfants" (2013). Honors Program Theses. 609.