Inequalities for cd-indices of joins and products of polytopes

Richard Ehrenborg, Harold Fox.

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join U circle inside V sign V and the cd-index of the Cartesian product U × V. As an application of these recurrences, we prove the inequality Ψ(U circle inside V sign (V circle inside V sign W)) ≤ Ψ((U circle inside V sign V) × W) involving the cd-indices of three polytopes.

Original languageEnglish
Pages (from-to)427-452
Number of pages26
Issue number3
StatePublished - 2003

Bibliographical note

Funding Information:
We thank Louis Bil l era, Margaret Readdy and the two referees for their generous comments. This research was partial l y supported by National Science Foundation DMS 96-19681 as part of an REU project at Cornel l University. The first author was also partially supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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