Abstracts
for the Seminar

Spring 2019

**Speaker: **Alexander Lazar, University of Miami

**Title: **The Intersection Lattice of the Homogenized Linial Arrangement

**Time:** 2:30 PM, Monday, March 18, 2019

**Place:** Malott 206

**Abstract:** Hetyei recently introduced a hyperplane arrangement (called the homogenized Linial arrangement) and used the finite field method of Athanasiadis to show that its number of regions is a median Genocchi number. These numbers count a class of permutations known as Dumont derangements. In joint work with Wachs, we take a different approach, which makes direct use of Zaslavsky's formula relating the intersection lattice of this arrangement to the number of regions. We refine Hetyei's result by obtaining a combinatorial interpretation of the Möbius function of this lattice in terms of variants of the Dumont permutations. The nonmedian Genocchi numbers appear in an unexpected way. Our techniques also yield type B, and more generally Dowling arrangement, analogs of these results

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