Speaker:  Gabor Hetyei, UNC Charlotte

Title:  Alternation acyclic tournaments and the homogeneous Linial arrangement

Abstract:

We define a tournament to be alternation acyclic if it does not

contain a cycle in which descents and ascents alternate. We show that

these label the regions in a homogenized generalization of the Linial

arrangement. Using a result by Athanasiadis, we show that these are

counted by the median Genocchi numbers. By establishing a bijection

with objects defined by Dumont, we show that alternation acyclic

tournaments in which at least one ascent begins at each vertex, except

for the largest one, are counted by the Genocchi numbers of the first

kind. As an unexpected consequence, we obtain a simple model for the

normalized median Genocchi numbers.