Lifting inequalities for polytopesRichard EhrenborgUniversity of Kentucky
February 19,

ABSTRACT


The fvector enumerates the number of faces of a convex polytope according to dimension. The flag fvector is a refinement of the fvector since it enumerates face incidences of the polytope. To classify the set of flag fvectors of polytopes is an open problem in discrete geometry. This was settled for 3dimensional polytopes by Steinitz a century ago. However, already in dimension 4 the problem is open. We will discuss the known linear inequalities for the flag fvector of polytopes. These inequalities include the nonnegativity of the toric gvector, that the simplex minimizes the cdindex, and the Kalai convolution of inequalities. We will introduce a method of lifting inequalities from lower dimensional polytopes to higher dimensions. As a result we obtain two new inequalities for 6dimensional polytopes. The talk will be accessible to a general audience. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

