Inequalities for cd-Indices of Joins and Products of Polytopes

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 \(U\textcircled{v}V\) and the cd-index of the Cartesian product U x V. As an application of these recurrences, we prove the inequality \( \psi {\left( {U{\kern 1pt} \textcircled{v}{\left( {V \times W} \right)}} \right)} \leqslant \psi {\left( {{\left( {U\textcircled{v}V} \right)} \times W} \right)} \) involving the cd-indices of three polytopes.

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Correspondence to Richard Ehrenborg.

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Ehrenborg, R., Fox, H. Inequalities for cd-Indices of Joins and Products of Polytopes. Combinatorica 23, 427–452 (2003). https://doi.org/10.1007/s00493-003-0026-z

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AMS Subject Classification (2000):

  • 06A07
  • 52B05