AProPo -- 15 f-Vector of Combinatorial Polytopes

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15 f-Vector of Combinatorial Polytopes

Input:	Vertex-facet incidence matrix of a polytope P
Output:	f-vector of P

Status (general):	Open
Status (fixed dim.):	Polynomial time

By the remarks on Problem 14, it is clear that the first k entries of the f-vector can be computed in polynomial time for every fixed k.

If the polytope is simplicial and a shelling (or a partition) of its boundary complex is available (see Problems 18 and 19), then one can compute the entire f-vector in polynomial time [66, Chap. 8].