Inequalities for the CD-Index

Richard Ehrenborg

Institute for Advanced Study

September 16,
refreshments at 3:45pm


We prove an inequality involving the cd-indices of a convex polytope P, a face F of the polytope and the link P/F. As a consequence we settle a conjecture of Stanley that the cd-index of d-dimensional polytopes is minimized on the d-dimensional simplex. Moreover, we show how this gives quadratic inequalities on the flag f-vector of polytopes. Lastly, we present an upper bound theorem for the cd-index of polytopes.

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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