Monotonicity of the cd-index for polytopes |
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| Authors: | Louis J Billera Richard Ehrenborg |
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| Institution: | (1) Department of Mathematics, White Hall, Cornell University, Ithaca, NY 14853-7901, USA (e-mail: billera@math.cornell.edu) , US;(2) School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA (e-mail: jrge@math.ias.edu) , US |
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| Abstract: | We prove that the cd-index of a convex polytope satisfies a strong monotonicity property with respect to the cd-indices of any face and its link. As a consequence, we prove for d-dimensional polytopes a conjecture of Stanley that the cd-index is minimized on the d-dimensional simplex. Moreover, we prove the upper bound theorem for the cd-index, namely that the cd-index of any d-dimensional polytope with n vertices is at most that of C(n,d), the d-dimensional cyclic polytope with n vertices.
Received September 29, 1998; in final form February 8, 1999 |
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