Relationships Among Flag f-Vector Inequalities for Polytopes

@article{Stenson2004RelationshipsAF,
  title={Relationships Among Flag f-Vector Inequalities for Polytopes},
  author={Catherine Stenson},
  journal={Discrete & Computational Geometry},
  year={2004},
  volume={31},
  pages={257-273}
}
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… CONTINUE READING