


Abstract: We will discuss an elementary proof of the formula for the number of factorizations of the cycle (1,2,3,..n) into a product of transpositions. The proof uses a bijection between the factorizations and ternary trees.
The bijection is easy to visualize, which allows for an easy generalization: counting factorizations into a_k cycles of length k, for a suitable vector (a_2, a_3, ...). Some harder generalizations will also be mentioned.
The problem arose in an applied context of semiclassical analysis of quantum transport through a chaotic cavity. Time permitting, I will give a short elementary explanation of the physics involved.
