# Michelle Wachs: On the homogenized Linial arrangement and Genocchi numbers

**Time: **
Wed 2019-10-16 10.15 - 11.00

**Lecturer: **
Michelle Wachs

**Location: **
Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Abstract: The homogenized Linial arrangement is a hyperplane

arrangement recently introduced by Gabor Hetyei, who showed that its

number of regions is a median Genocchi number. Using a different

method, we refine Hetyei's result by providing a combinatorial

interpretation of the coefficients of the characteristic polynomial of

the intersection lattice of this arrangement in terms of Dumont-like

permutations. This enables us to derive formulas for the generating

function of the characteristic polynomial, which reduce to known

formulas for the generating functions of the Genocchi numbers and the

median Genocchi numbers. Our techniques also yield type B analogs of

these results, and Dowling arrangement generalizations. As a byproduct

of our work, we obtain new models for the Genocchi and median Genocchi

numbers. This is joint work with Alex Lazar.