volume 31, issue 2, P257-273 2004
DOI: 10.1007/s00454-003-0756-0
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Abstract: Abstract. We examine linear inequalities satisfied by the flag f -vectors of polytopes. One source of these inequalities is the toric g-vector; convolutions of its entries are nonnegative for rational polytopes. We prove a conjecture of Meisinger about a redundancy in these inequalities. Another source of inequalities is the cd-index; among all d-polytopes, each cd-index coefficient is minimized on the d-simplex. We show that not all of the cdindex inequalities are implied by the toric g-vector inequalities, …

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