Lifting inequalities for polytopes

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15 Scopus citations


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 languageEnglish
Pages (from-to)205-222
Number of pages18
JournalAdvances in Mathematics
Issue number1
StatePublished - 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.


  • Flag f-vector
  • Linear inequalities
  • Toric g-vector
  • cd-index

ASJC Scopus subject areas

  • General Mathematics

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