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A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes

1981; Elsevier BV; Volume: 31; Issue: 3 Linguagem: Inglês

10.1016/0097-3165(81)90058-3

1096-0899

Louis J. Billera, Carl W. Lee,

Point processes and geometric inequalities

The f-vector of a convex d-polytope P is the vector f(P) = (f0(P), f1(P),…, fd − 1(P)), where fj(P) is the number of j-dimensional faces of P. McMullen in 1971 proposed a characterization of the set of all f-vectors of simplicial convex d-polytopes. In 1979 the authors announced the sufficiency of the characterization and Stanley proved its necessity. We give here a proof of the sufficiency of McMullen's conditions.