There is no pre-seminar.

Gessel defined a four parameter family of polynomials associated with rooted labeled binary trees of a fixed size using ascents and descents, and noticed that certain evaluations of this family give the number of regions in well-known hyperplane arrangements such as the braid arrangement, the Catalan arrangement, the Shi arrangement and the Linial arrangement.

I will give an alternate description for this family of polynomials using a generalization of the excedance statistic on permutations, and then proceed to give a few enumerative results of a rook-theoretic flavour.