Abstract
We present a method of lifting linear inequalities for the flag f-vector of polytopes to higher dimensions. Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index. We obtain new inequalities for six-dimensional polytopes. In the last section we present the currently best known inequalities for dimensions 5 through 8.
| Original language | English |
|---|---|
| Pages (from-to) | 205-222 |
| Number of pages | 18 |
| Journal | Advances in Mathematics |
| Volume | 193 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1 2005 |
Bibliographical note
Funding Information:The author was partially supported by National Science Foundation grant 0200624. I would like to thank the MIT Mathematics Department for their kind support where this research was initiated while the author was a Visiting Scholar. I also thank the Institute for Advanced Study where the calculations were carried out. The author also thanks Margaret Readdy for many helpful suggestions and the two referees for useful comments.
Keywords
- Flag f-vector
- Linear inequalities
- Toric g-vector
- cd-index
ASJC Scopus subject areas
- General Mathematics