Jun 30, 2017
Friday

01:00 PM  02:00 PM


The DehnSommerville Relations and the Catalan Matroid
Anastasia Chavez (University of California, Berkeley)

 Location
 MSRI: Baker Board Room
 Video


 Abstract
The fvector of a ddimensional polytope P stores the number of faces of each dimension. When P is simplicial the DehnSommerville relations condense the fvector into the gvector, which has length ⌈d+12⌉. Thus, to determine the fvector of P, we only need to know approximately half of its entries. This raises the question: Which (⌈d+12⌉)subsets of the fvector of a general simplicial polytope are sufficient to determine the whole fvector? We prove that the answer is given by the bases of the Catalan matroid.
 Supplements



