Wednesday, October 03, 2018 at 4:15pm to 5:15pm
SPEAKER: Tamas Kalman (Tokyo Institute of Technology)
TITLE: Hypergraph polynomials and the Bernardi process
The product of two simplices can be triangulated by non-crossing trees. I will start with a generalization of this fact: the root polytope of an arbitrary bipartite graph has a dissection by a simple class of spanning trees derived from a ribbon structure. Moreover, the dissection comes with a natural shelling order. The resulting h-vector is equivalent to (a) the Ehrhart polynomial of the root polytope and thus, by earlier joint work with Postnikov, to the common 'interior polynomial' of the two hypergraphs induced by the bipartite graph (b) a new variant of the interior polynomial, defined using the ribbon structure along the lines of Bernardi's approach to the Tutte polynomial. Hence we obtain a Bernardi-type definition of the interior polynomial. This is joint work with Lilla Tóthmérész.