Seminar

I will speak about Zonotopal algebras, which were defined for arbitrary zonotopes. There are three types of these algebras: external, central, and internal. These algebras have a number of interesting properties. Their Hilbert series are specializations of the corresponding Tutte polynomial. In the case of unimodular zonotopes: the total dimensions are the number of lattice points, the volume, and the number of interior lattice points resp. In the graphical case: the first two algebras enumerate spanning forests and trees. I will focus more on the external case, which is more natural. In fact, an external zonotopal algebra remembers the combinatorial structure of its zonotope.