Discrete Mathematics Seminar: Counting Transitive Factorizations in the Symmetric Group

Abstract

Transitive factorizations in the symmetric group have recently become objects of intense interest because of their connections with algebraic geometry. We shall briefly discuss these geometric connections, but our view of permutation factorization will be purely combinatorial. In particular, we will show how a simple graphical model can be exploited to count various classes of transitive factorizations.