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.
|Number of pages||18|
|Journal||Advances in Mathematics|
|State||Published - May 1 2005|
Bibliographical noteFunding 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.
- Flag f-vector
- Linear inequalities
- Toric g-vector
ASJC Scopus subject areas
- Mathematics (all)