Invertible relations on polytopes

Abstract

If g and h are any nonzero functions on the class of convex polytopes then α(Fi, Fj) =g(Fi)/h(Fj) is a valuation whose inverse is ω(Fi, Fj) = (-1)j-ih(Fi)/g(Fj). This is proved and a smaller class of valuations are characterized: those α(Fi, Fj) which depend only on i and j and which have inverses of the same form. © 1987 Springer-Verlag New York Inc.