  The number of minimal transitive star factorizations of a permutation was
shown by Irving and Rattan to depend only on the conjugacy class of the
permutation, a surprising result given that the pivot plays a very particular
role in such factorizations. Here, we explain this symmetry and provide a
bijection between minimal transitive star factorizations of a permutation \pi
having pivot k and those having pivot k'.

Combinatorics